Class 6 Ganita Prakash Chapter 6 Perimeter and Area Solutions

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Class 6 Ganita Prakash · Chapter 6
Perimeter and Area

Page-wise textbook solutions (pages 129–150) · Every step · Figures · Common mistakes · Tips

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🗝️ Key ideas of this chapter

• Perimeter = length of the boundary. Rectangle: 2 × (l + b). Square: 4 × side. Triangle: sum of the three sides. Regular polygon: number of sides × side.
• Area = region enclosed, in square units. Rectangle: l × b. Square: side × side.
• Odd shapes: split into rectangles (add) or box-and-subtract.
• A triangle drawn inside a rectangle on the same base = half the rectangle.
• Same area can have different perimeters (and the other way round). Long thin → more perimeter; square-like → less.

📖 Textbook Page 129

📖 Page 129Perimeter of a rectangle

Find the perimeter of rectangle ABCD with length 12 cm and breadth 8 cm.

Rectangle ABCD

1Perimeter = AB + BC + CD + DA.

2Opposite sides are equal, so perimeter = 2 × (length + breadth).

3= 2 × (12 + 8) = 2 × 20 = 40 cm.

✅ Answer: 40 cm

⚠️ Common mistake: Adding only two sides (12 + 8 = 20). The boundary has four sides.

📖 Textbook Page 130

📖 Page 130Perimeter of a square

Debojeet puts coloured tape all around a square photo frame of side 1 m. How much tape does he need?

A square photo frame of side 1 m with tape all around.

1Tape all around = perimeter of the square.

2All four sides are equal: 4 × 1 m = 4 m.

✅ Answer: 4 m

📖 Textbook Page 131

📖 Page 131Perimeter of a triangle

Find the perimeter of a triangle with sides 4 cm, 5 cm and 7 cm.

Triangle with sides 4 cm, 5 cm, 7 cm.

1Perimeter of a triangle = sum of its three sides.

24 + 5 + 7 = 16 cm.

✅ Answer: 16 cm

📖 Page 131Example · Lace on a tablecloth

Akshi puts lace all around a tablecloth 3 m long and 2 m wide. How much lace is needed?

1Lace all around = perimeter.

22 × (3 + 2) = 2 × 5 = 10 m.

✅ Answer: 10 m

📖 Page 131Example · Rounds of a park

Usha takes three rounds of a square park of side 75 m. How far does she walk?

1One round = 4 × 75 = 300 m.

2Three rounds = 3 × 300 = 900 m.

✅ Answer: 900 m

📖 Textbook Page 132

📖 Page 132Figure it Out · Q1

Find the missing terms: (a) perimeter of rectangle 14 cm, breadth 2 cm, length = ? (b) perimeter of square 20 cm, side = ? (c) perimeter of rectangle 12 m, length 3 m, breadth = ?

1(a) length + breadth = 14 ÷ 2 = 7, so length = 7 − 2 = 5 cm.

2(b) side = 20 ÷ 4 = 5 cm.

3(c) length + breadth = 12 ÷ 2 = 6, so breadth = 6 − 3 = 3 m.

✅ Answer: (a) 5 cm (b) 5 cm (c) 3 m

💡 Tip: Halve the perimeter first — that gives length + breadth.

📖 Page 132Figure it Out · Q2

A rectangle with sides 5 cm and 3 cm is made of wire. The wire is bent into a square. What is the side of the square?

1Length of wire = perimeter of rectangle = 2 × (5 + 3) = 16 cm.

2Same wire makes the square: side = 16 ÷ 4 = 4 cm.

Wire 16 cm long

Same wire bent into a square of side 4 cm

✅ Answer: 4 cm

📖 Page 132Figure it Out · Q3

A triangle has perimeter 55 cm and two sides 20 cm and 14 cm. Find the third side.

120 + 14 = 34 cm.

2Third side = 55 − 34 = 21 cm.

✅ Answer: 21 cm

📖 Page 132Figure it Out · Q4

Find the cost of fencing a rectangular park 150 m long and 120 m wide at ₹40 per metre.

1Perimeter = 2 × (150 + 120) = 2 × 270 = 540 m.

2Cost = 540 × 40 = ₹21,600.

✅ Answer: ₹21,600

📖 Page 132Figure it Out · Q5

A string 36 cm long is used to make (a) a square (b) an equilateral triangle (c) a regular hexagon. Find the length of each side.

1(a) 36 ÷ 4 = 9 cm.

2(b) 36 ÷ 3 = 12 cm.

3(c) 36 ÷ 6 = 6 cm.

✅ Answer: (a) 9 cm (b) 12 cm (c) 6 cm

📖 Page 132Figure it Out · Q6

A field 230 m long and 160 m wide is fenced with 3 rounds of rope. Find the total length of rope.

Field 230 m × 160 m fenced with 3 rounds of rope.

1One round = 2 × (230 + 160) = 2 × 390 = 780 m.

2Three rounds = 3 × 780 = 2340 m.

✅ Answer: 2340 m

📖 Textbook Page 133

📖 Page 133Matha Pachchi · Q1

Akshi runs 5 rounds of the outer track (70 m × 40 m). Find her total distance.

Two rectangular tracks; both girls start at the bottom-right corner.

1One round = 2 × (70 + 40) = 220 m.

25 rounds = 5 × 220 = 1100 m.

✅ Answer: 1100 m

📖 Page 133Matha Pachchi · Q2

Toshi runs 7 rounds of the inner track (60 m × 30 m). Find her distance. Who ran more?

1One round = 2 × (60 + 30) = 180 m.

27 rounds = 7 × 180 = 1260 m.

31260 m > 1100 m.

✅ Answer: Toshi ran 1260 m — she ran 160 m more than Akshi.

📖 Page 133Matha Pachchi · Q3

Mark A, B, C where Akshi is after 250 m, 500 m and 1000 m, and X, Y, Z where Toshi is after 250 m, 500 m and 1000 m. How many full rounds after 1000 m?

1Both start at the bottom-right corner and run along the bottom side first (as the arrows show).

2Akshi (220 m a round): 250 = 220 + 30 → A is 30 m along the bottom side.

3500 = 2 × 220 + 60 → B is 60 m along the bottom side.

41000 = 4 × 220 + 120 → 4 full rounds; 120 = 70 (bottom) + 40 (left side) + 10 → C is 10 m along the top side.

5Toshi (180 m a round): 250 = 180 + 70 = 60 (bottom) + 10 → X is 10 m up the left side.

6500 = 2 × 180 + 140 = 60 + 30 + 50 → Y is 50 m along the top side.

71000 = 5 × 180 + 100 = 60 + 30 + 10 → 5 full rounds; Z is 10 m along the top side.

A, B, C: Akshi after 250 m, 500 m, 1000 m. X, Y, Z: Toshi after 250 m, 500 m, 1000 m.

✅ Answer: Akshi: 4 full rounds by 1000 m; Toshi: 5 full rounds. See the marked points.

💡 Tip: Take away full rounds first; then walk the leftover metres side by side.

📖 Textbook Page 134

📖 Page 134Deep Dive · Common finishing line

Square tracks: inner 100 m a side, outer 150 m a side. The finishing line is at the middle of the bottom side. For a 350 m race, where should A (inner) and B (outer) start?

Two square tracks with a common finishing line in the middle of the bottom side.

1Inner round = 4 × 100 = 400 m. Running 350 m to the line = starting 400 − 350 = 50 m ahead of the line (in the running direction).

2The line is 50 m from the bottom-right corner → A is at the bottom-right corner of the inner track.

3Outer round = 4 × 150 = 600 m. Start 600 − 350 = 250 m ahead of the line.

4From the line: 75 m to the corner + 150 m up the right side = 225 m; 25 m more along the top → B is 25 m from the top-right corner.

A: inner start (corner, 50 m before the line along the track direction reversed). B: outer start (25 m from the top-right corner).

✅ Answer: A: bottom-right corner of the inner track. B: on the top side of the outer track, 25 m from the top-right corner.

📖 Page 134Estimate and Verify

Cut a few random shapes from paper. Estimate each perimeter, then measure with a thread and a scale.

1Lay a thread along the boundary, mark the end, straighten it and measure.

2Compare with your estimate; estimates get better with practice.

✅ Answer: Activity — answers depend on your shapes.

📖 Page 134Akshi or Toshi?

On a dot grid a right triangle has two sides of 3 units and a slanting side. Akshi says the perimeter is 9 units; Toshi says it is more. Who is right?

The triangle on a dot grid.

1The two straight sides are 3 + 3 = 6 straight units.

2The slanting side crosses 3 dot squares diagonally: each diagonal is longer than a straight unit.

3So the perimeter is 6s + 3d, which is more than 9 units.

✅ Answer: Toshi is right: perimeter = 6s + 3d, more than 9 units.

📖 Textbook Page 135

📖 Page 135Straight and diagonal units

Write the perimeters of the purple, pink, green and brown shapes using straight (s) and diagonal (d) units.

Purple, pink, green and brown shapes on a dot grid.

1Count the red (straight) and blue (diagonal) edges of each shape.

2Purple: 8 straight, 2 diagonal.

3Pink: 4 straight, 6 diagonal.

4Green: 12 straight, 6 diagonal.

5Brown: 18 straight, 6 diagonal.

Red = straight units, blue = diagonal units.

✅ Answer: Purple 8s + 2d · Pink 4s + 6d · Green 12s + 6d · Brown 18s + 6d

📖 Page 135Square and equilateral triangle

What is similar between a square and an equilateral triangle?

1Both have all sides equal and all angles equal — both are regular polygons.

2So perimeter = number of sides × length of one side (4 × side, 3 × side).

✅ Answer: Both are regular polygons; perimeter = number of sides × side.

📖 Textbook Page 136

📖 Page 136Regular polygons

Find the perimeter of regular shapes around you and write a general rule.

1A regular pentagon of side 5 cm: 5 × 5 = 25 cm. A regular hexagon of side 3 cm: 6 × 3 = 18 cm.

✅ Answer: Perimeter of a regular polygon = number of sides × length of one side.

📖 Page 136Split and rejoin

A 6 cm × 4 cm chit is cut into two 6 cm × 2 cm pieces. Arrangement (a) has perimeter 28 cm. Find the perimeters of (b), (c) and (d).

A 6 cm × 4 cm chit is cut into two 6 cm × 2 cm pieces.

(a) 28 cm

(b)

(c)

(d)

1Each piece has perimeter 2 × (6 + 2) = 16 cm; two pieces = 32 cm.

2When pieces touch, the touching length is lost twice (once from each piece).

3(b) touching length 2 cm → 32 − 4 = 28 cm.

4(c) touching length 2 cm → 32 − 4 = 28 cm.

5(d) touching length 3 cm → 32 − 6 = 26 cm.

✅ Answer: (b) 28 cm (c) 28 cm (d) 26 cm

💡 Tip: Perimeter of joined shape = total of both perimeters − 2 × touching length.

📖 Page 136Perimeter 22 cm

Arrange the two pieces to make a figure with perimeter 22 cm.

1We need 32 − 22 = 10 cm lost, so the touching length must be 10 ÷ 2 = 5 cm.

2Put the two long sides together, sliding one piece 1 cm up: they touch along 5 cm.

Touching length 5 cm → 32 − 10 = 22 cm

✅ Answer: Place them side by side, shifted by 1 cm (touching along 5 cm).

📖 Textbook Page 137

📖 Page 137Area formulas

Fill in: Area of a square = ____; Area of a rectangle = ____.

1On squared paper, a 4 × 3 rectangle has 3 rows of 4 squares = 12 squares.

2So area = length × breadth; for a square, side × side.

✅ Answer: Area of a square = side × side; Area of a rectangle = length × breadth.

📖 Page 137Example · Carpet

A floor is 5 m × 4 m. A square carpet of side 3 m is laid on it. Find the area not carpeted.

Floor 5 m × 4 m with a 3 m × 3 m carpet.

1Floor = 5 × 4 = 20 sq m.

2Carpet = 3 × 3 = 9 sq m.

3Not carpeted = 20 − 9 = 11 sq m.

✅ Answer: 11 sq m

📖 Textbook Page 138

📖 Page 138Example · Flower beds

Four square flower beds of side 4 m are at the corners of land 12 m × 10 m. Find the remaining area.

Land 12 m × 10 m with four 4 m × 4 m flower beds at the corners.

1Land = 12 × 10 = 120 sq m.

2One bed = 4 × 4 = 16 sq m; four beds = 64 sq m.

3Remaining = 120 − 64 = 56 sq m.

✅ Answer: 56 sq m

📖 Page 138Figure it Out · Q1

A rectangular garden is 25 m long and has area 300 sq m. Find its width.

1Area = length × width, so width = 300 ÷ 25.

2300 ÷ 25 = 12 m.

✅ Answer: 12 m

📖 Page 138Figure it Out · Q2

Find the cost of tiling a plot 500 m × 200 m at ₹8 per hundred sq m.

1Area = 500 × 200 = 1,00,000 sq m.

2Number of hundreds = 1,00,000 ÷ 100 = 1000.

3Cost = 1000 × 8 = ₹8000.

✅ Answer: ₹8000

⚠️ Common mistake: Multiplying 1,00,000 by 8 — the rate is per HUNDRED sq m.

📖 Page 138Figure it Out · Q3

A coconut grove is 100 m × 50 m. Each tree needs 25 sq m. Find the largest number of trees.

1Area = 100 × 50 = 5000 sq m.

2Trees = 5000 ÷ 25 = 200.

✅ Answer: 200 trees

📖 Page 138Figure it Out · Q4

Split the figures into rectangles and find their areas (in metres).

(a) all measures in metres

(b) all measures in metres

1(a) Cut across: bottom 3 × 3 = 9, next strip 7 × 1 = 7, then 5 × 2 = 10, top 2 × 1 = 2.

2(a) Total = 9 + 7 + 10 + 2 = 28 sq m.

3(b) Two legs 1 × 3 = 3 each and the top 3 × 1 = 3.

4(b) Total = 3 + 3 + 3 = 9 sq m (or 5 × 3 − 3 × 2 = 15 − 6 = 9).

Shape (a) — split into rectangles

Shape (b) — split into rectangles

✅ Answer: (a) 28 sq m (b) 9 sq m

📖 Textbook Page 139

📖 Page 139Tangram · Q1

Which tangram pieces have the same area?

The seven tangram pieces in a square.

1Place pieces over each other.

2A and B (big triangles) match. C and E (small triangles) match.

3D, F and G are each made of two small triangles.

Areas in terms of shape C.

✅ Answer: A = B; C = E; D = F = G.

📖 Page 139Tangram · Q2

How many times bigger is D than C? How are C, D and E related?

1C and E together cover D exactly.

✅ Answer: D is 2 times C; D = C + E.

📖 Page 139Tangram · Q3

Which has more area: D or F?

1D = C + E = 2C.

2F is also covered by two small triangles = 2C.

✅ Answer: Same area (each = 2C).

📖 Page 139Tangram · Q4

Which has more area: F or G?

1G (the parallelogram) can be covered by two small triangles = 2C.

2F = 2C.

✅ Answer: Same area (each = 2C).

📖 Page 139Tangram · Q5

What is the area of A compared to G?

1A can be covered by F + C + E = 2C + C + C = 4C.

2G = 2C, so A = 2 × G.

✅ Answer: A is twice as big as G (A = 4C, G = 2C).

📖 Page 139Tangram · Q6

What is the area of the big square in terms of C?

1A + B + C + D + E + F + G = 4C + 4C + C + 2C + C + 2C + 2C.

2= 16C.

✅ Answer: 16 times C (16C)

📖 Page 139Tangram · Q7

Arrange the 7 pieces into a rectangle. What is its area in terms of C?

1The same 7 pieces are used; nothing is added or removed.

2So the area does not change: 16C.

The seven pieces rearranged into a rectangle — area is still 16 C.

✅ Answer: 16C — same pieces, same area.

📖 Page 139Tangram · Q8

Are the perimeters of the square and the rectangle the same?

1If the square has side 4 units, its perimeter is 16 units.

2The rectangle is about 5.7 × 2.8 units; its perimeter is about 17 units.

3Pieces touch along different edges, so the outer boundary changes.

✅ Answer: Different — same area does not mean same perimeter (the rectangle’s is a little longer).

📖 Textbook Page 140

📖 Page 140Estimating area

How do we estimate the area of a curvy shape on squared paper?

1Count full squares as 1 sq unit.

2Count more-than-half squares as 1; ignore less-than-half squares.

3Count exactly-half squares as ½.

✅ Answer: Trace on squared paper and use the four counting rules.

📖 Page 140Find the areas

Find the areas of the purple, pink, green and brown dot-grid shapes (1 square = 1 sq unit).

Same shapes as on page 135.

1Count full squares and join half squares (each diagonal cuts a square into two halves).

2Purple: 3 full + 2 halves = 4. Pink: 12 − 6 halves = 9.

3Green: 7 full + 6 halves = 10. Brown: 8 full + 6 halves = 11.

✅ Answer: Purple 4, pink 9, green 10, brown 11 sq units.

📖 Textbook Page 141

📖 Page 141Let’s Explore · Why squares?

Why do we measure area with squares and not circles?

1Circles leave gaps; the same rectangle holds 42 or 44 circles depending on packing.

2Squares fit together with no gaps or overlaps, and fit neatly along straight edges.

3Squares make the rule length × breadth work.

✅ Answer: Squares tile without gaps or overlaps, so counts are exact and easy.

📖 Page 141Corridor and playground

Find the area of the floor outside your classroom corridor and of your school playground.

1Measure length and breadth with a measuring tape.

2Area = length × breadth (split odd shapes into rectangles).

✅ Answer: Activity — depends on your school.

📖 Page 141Rectangles of area 24

Make all rectangles with whole-number sides and area 24 sq units. Which has the greatest perimeter? The least?

1Pairs: 1 × 24, 2 × 12, 3 × 8, 4 × 6.

2Perimeters: 50, 28, 22, 20.

All rectangles of area 24

✅ Answer: Greatest: 1 × 24 (50 units). Least: 4 × 6 (20 units).

📖 Textbook Page 142

📖 Page 142Area 32 sq cm

Repeat for area 32 sq cm. Can you predict the shapes with the greatest and least perimeter?

11 × 32 (P 66), 2 × 16 (P 36), 4 × 8 (P 24).

2Long thin rectangles have the greatest perimeter; the most square-like has the least.

✅ Answer: Greatest 1 × 32 (66 cm); least 4 × 8 (24 cm). Thinnest → most perimeter; closest to a square → least.

📖 Page 142Area of a triangle · Diagonal

Cut a rectangle along a diagonal. Do the two triangles overlap exactly? What can you conclude?

1The two triangles fit exactly on each other.

2So each triangle is half of the rectangle.

✅ Answer: Yes — each triangle = half the area of the rectangle.

📖 Page 142Blue rectangle and yellow triangle

Is the blue rectangle’s area more, less or the same as the yellow triangle’s?

A rectangle and a triangle made from its two halves.

1The triangle is made of the two halves of the rectangle (cut along the diagonal) joined differently.

2Nothing added, nothing removed.

✅ Answer: Same area.

📖 Textbook Page 143

📖 Page 143Triangles BAD and ABE

Find the areas of the blue triangle BAD and red triangle ABE on the grid.

Rectangle ABCD on a grid: triangle BAD (blue) and triangle ABE (red).

1Rectangle ABCD = 5 × 4 = 20 sq units.

2BAD is half of ABCD (cut on a diagonal) = 10.

3ABE = half of AFED + half of BFEC = ½ × 12 + ½ × 8 = 6 + 4 = 10.

✅ Answer: Both are 10 sq units — half of the rectangle (20 sq units).

📖 Textbook Page 144

📖 Page 144Conclusion

Write the conclusion about triangles inside a rectangle.

1Both triangles have the same base (AB) and reach the opposite side.

✅ Answer: A triangle with base on one side of a rectangle and top on the opposite side has half the area of the rectangle.

📖 Page 144Figure it Out · Q1

Find the areas of figures a–e by splitting them into rectangles and triangles.

Figures a–e on squared paper (1 square = 1 sq unit).

1a: a 4 × 5 rectangle in the middle + 2 triangles (½ × 4 × 1 each) → 20 + 2 + 2 = 24.

2b: rectangle 4 × 5 + top triangle ½ × 4 × 3 + bottom triangle ½ × 4 × 2 → 20 + 6 + 4 = 30.

3c: draw a box 6 × 12 = 72 around it; take away the 4 corner triangles 3 + 3 + 15 + 3 = 24 → 72 − 24 = 48.

4d: box 4 × 5 = 20 minus the notch triangle ½ × 4 × 2 = 4 → 16.

5e: box 4 × 6 = 24 minus 4 corner triangles 2 + 2 + 2 + 6 = 12 → 12.

Areas found by splitting into rectangles and triangles.

✅ Answer: a 24 · b 30 · c 48 · d 16 · e 12 sq units

💡 Tip: Box-and-subtract: draw the smallest rectangle around the shape, then take away the right triangles at the corners.

📖 Textbook Page 145

📖 Page 145Making it More or Less

Using 9 unit squares: (1) smallest perimeter? (2) largest? (3) make perimeter 18. (4) Is each shape unique?

1(1) The 3 × 3 square is the most compact → 12 units.

2(2) Each square joined to the next by only one side → a line or any ‘snake’ → 20 units.

3(3) Each extra shared side cuts 2 units from 20. Make one 2 × 2 block with a tail of 5 squares → 18 units.

4(4) 12: only the 3 × 3 square. 20 and 18: many shapes (any line, L or snake gives 20; many shapes give 18).

✅ Answer: (1) 12 (2) 20 (3) e.g. a 2 × 2 block with a tail of 5 squares (4) only 12 is unique.

📖 Page 145Adding a square

A figure has perimeter 24 units. A new square is attached as shown. What happens to the perimeter? Can you make it increase, decrease or stay the same?

Perimeter = 24 units

1Each new square adds 4 sides but hides 2 sides for every side it shares.

2In the corner shown it touches 2 squares: +4 − 4 = 0 → stays 24.

3Touching 1 side: +4 − 2 = +2 (increases). Touching 3 sides: +4 − 6 = −2 (decreases).

New square in the gap: still 24 units

✅ Answer: In the gap shown it stays 24. One side touching → 26; three sides touching → 22.

📖 Textbook Page 146

📖 Page 146Charan’s house

Charan’s house is on a rectangular plot 30 ft tall. Find the missing measurements and the area of his house.

Charan’s house plan (redrawn). Some measurements are given.

1Small bedroom: 180 ÷ 15 = 12 ft → 15 ft × 12 ft.

2Left side: 15 + 12 = 27, so the garden strip is 30 − 27 = 3 ft tall.

3Width of plot = 15 (bedrooms) + 5 (toilet) + 15 (kitchen) = 35 ft.

4Utility: 15 − 12 = 3 ft tall → 15 × 3 = 45 sq ft.

5Garden: 20 × 3 = 60 sq ft. Parking: 15 × 3 = 45 sq ft.

6Hall (L-shape): 20 × 12 + 5 × 5 = 240 + 25 = 265 sq ft.

7House = 35 × 30 = 1050 sq ft. Check: 225 + 50 + 45 + 180 + 180 + 265 + 60 + 45 = 1050 ✔

Charan’s house (35 ft × 30 ft = 1050 sq ft) — answers in red.

✅ Answer: Missing: small bedroom 12 ft, utility 15 × 3, garden 20 × 3, parking 15 × 3, hall 265 sq ft. House area = 1050 sq ft.

📖 Textbook Page 147

📖 Page 147Sharan’s house

Find the missing measurements and the area of Sharan’s house (width 42 ft). Compare with Charan’s house.

Sharan’s house plan (redrawn). Some measurements are given.

1Height = 15 + 10 = 25 ft (master + small bedroom).

2Small bedroom = 12 × 10 = 120 sq ft.

3Hall height = 25 − 10 = 15 ft → 23 × 15 = 345 sq ft.

4Toilet width = 23 − 18 = 5 ft → 5 × 10 = 50 sq ft.

5Utility width = 42 − 12 − 23 = 7 ft → 7 × 10 = 70 ✔. Entrance = 7 × 15 = 105 sq ft.

6House = 42 × 25 = 1050 sq ft. Perimeter: Sharan 2 × (42 + 25) = 134 ft; Charan 2 × (35 + 30) = 130 ft.

Sharan’s house (42 ft × 25 ft = 1050 sq ft) — answers in red.

✅ Answer: House area 1050 sq ft — the same as Charan’s. Perimeters differ: 134 ft vs 130 ft.

💡 Tip: Same area, different perimeters — the main idea of this chapter!

📖 Textbook Page 148

📖 Page 148Area Maze (a)

Find the missing area.

Area maze (a)

1Left and right columns have the same heights.

2Top row: 26 ÷ 13 = 2, so the right column is 2 times as wide.

3Bottom right = 2 × 15 = 30 sq cm.

Area maze (a) — solved

✅ Answer: 30 sq cm

📖 Page 148Area Maze (b)

Find the missing area.

Area maze (b)

1Bottom rectangle: 10 ÷ 2 = 5 cm long.

2Tall strip width = 5 − 3 = 2 cm, so its height = 10 ÷ 2 = 5 cm.

3Pink square height = 5 − 2 = 3 cm, width 3 cm → 9 sq cm.

Area maze (b) — solved

✅ Answer: 9 sq cm

📖 Page 148Area Maze (c)

Find the missing area.

Area maze (c)

1Middle: 42 ÷ 6 = 7 cm wide.

2Bottom: width 7 + 5 = 12 cm, height 60 ÷ 12 = 5 cm.

3Top square: height 15 − 6 − 5 = 4 cm, width 7 − 3 = 4 cm → 16 sq cm.

Area maze (c) — solved

✅ Answer: 16 sq cm

📖 Page 148Area Maze (d)

Find the missing length.

Area maze (d)

1Small rectangle: height = 18 ÷ 5 = 3.6 cm.

2Tall rectangle height = 4 + 3.6 = 7.6 cm.

3Width = 38 ÷ 7.6 = 5 cm.

Area maze (d) — solved

✅ Answer: 5 cm

📖 Textbook Page 149

📖 Page 149Figure it Out · Q1

Give the dimensions of a rectangle whose area is the sum of the areas of rectangles 5 m × 10 m and 2 m × 7 m.

150 + 14 = 64 sq m.

2Any pair multiplying to 64: 8 × 8, 16 × 4, 32 × 2.

✅ Answer: 64 sq m, e.g. 16 m × 4 m (or 8 m × 8 m).

📖 Page 149Figure it Out · Q2

A garden 50 m long has area 1000 sq m. Find its width.

11000 ÷ 50 = 20.

✅ Answer: 20 m

📖 Page 149Figure it Out · Q3

A room floor is 5 m × 4 m with a 3 m × 3 m carpet. Find the area not carpeted.

120 − 9 = 11.

✅ Answer: 11 sq m

📖 Page 149Figure it Out · Q4

Four flower beds 2 m × 1 m are dug at the corners of a garden 15 m × 12 m. How much area is left for the lawn?

1Garden = 15 × 12 = 180 sq m.

2Beds = 4 × (2 × 1) = 8 sq m.

3Lawn = 180 − 8 = 172 sq m.

Garden 15 m × 12 m with four 2 m × 1 m beds.

✅ Answer: 172 sq m

📖 Page 149Figure it Out · Q5

Shape A has area 18 sq units and Shape B has area 20 sq units, but A has a longer perimeter. Draw such shapes.

1A long thin strip has a big perimeter: 1 × 18 → perimeter 38.

2A compact rectangle has a small perimeter: 4 × 5 → perimeter 18.

Shape A: 18 squares in a long strip (P = 38). Shape B: 4 × 5 rectangle (20 squares, P = 18).

✅ Answer: e.g. A = 1 × 18 strip (P 38), B = 4 × 5 rectangle (P 18).

📖 Page 149Figure it Out · Q6

On a page, draw a border 1 cm from top and bottom and 1.5 cm from left and right. Find its perimeter.

1Measure your page, e.g. 20 cm × 28 cm.

2Border length = 20 − 3 = 17 cm; border height = 28 − 2 = 26 cm.

3Perimeter = 2 × (17 + 26) = 86 cm.

4Rule: perimeter of border = page perimeter − 2 × 3 − 2 × 2 = page perimeter − 10 cm.

A page with a border 1 cm from top and bottom, 1.5 cm from the sides.

✅ Answer: Page perimeter − 10 cm (for a 20 cm × 28 cm page: 86 cm).

📖 Page 149Figure it Out · Q7

Draw a 12 × 8 rectangle. Inside it, without touching, draw a rectangle with exactly half the area.

1Big area = 96, half = 48.

248 = 8 × 6 fits inside with space on all sides (12 > 8, 8 > 6).

An 8 × 6 rectangle (48 sq units) inside a 12 × 8 rectangle (96 sq units).

✅ Answer: e.g. an 8 × 6 rectangle (48 sq units).

📖 Page 149Figure it Out · Q8

A square is folded in half and cut into two rectangles. Which statement is always true? (a) each rectangle has more area than the square (b) the square’s perimeter is more than both rectangles’ together (c) both rectangles’ perimeters together = 1½ times the square’s (d) the square’s area is 3 times both rectangles’ together

1Take side 4: square perimeter 16, area 16.

2Each rectangle 4 × 2: perimeter 12; together 24.

324 ÷ 16 = 1½. True for any size: together = 6 × side, square = 4 × side.

4(a) false (each is half). (b) false (24 > 16). (d) false (areas are equal).

A square of side 4 cut into two 4 × 2 rectangles.

✅ Answer: (c)

🌍 Where do we use this?

• Fencing, lace, tiles, carpets, painting walls, house plans, sports tracks.

🚀 Link to higher classes

• Class 7: area of parallelograms and triangles (½ × base × height). Class 8: area of trapeziums and circles.

⬆ Top 🏠 Class 6 Hub

🔑 keytoenjoylearningmaths.blogspot.com · Solutions written in our own words, based on NCERT Ganita Prakash Class 6 (Grade 6)