Class 08 Activity – Surface Area 

Objective: 

To Verify the formula for area of a rhombus. Or to verify the following formula: Area of rhombus = 1/2 x product of its diagonals. 

Materials Required:

 gluestick,  Squared paper,  white sheet of paper, colour pencils, a pair of scissors, etc.,

Procedure: 

1. On a squared paper, draw a rhombus ABCD. Join its diagonals AC and BD, which. Intersect each other at o. Colour the four triangles so obtained using different colours.

2. Using a pair of scissors, cut out the four triangles. The cut outs so obtained are four congruent right triangular cut outs. Let the sides forming the right angle of each cut be x and y.

3. Arrange the four triangular cut-outs to form a rectangle as shown below.

Observations: 

Figure 3 is a rectangle of sides (x + x) and y or 2x and y.

So, area of this rectangle 

= 2x x y 

= 1/2 x 2x x 2y

= 1/2 x BD X AC

 [ From figure 1, 2x = BD and 2y = AC]

But, area of rectangle in figure 3 = area of rhombus (ABCD) in figure.

Or area of rhombus ABCD = 1/2 x BD X AC = 1/2 x product of its diagonals.

Conclusion: 

From the above activity, it is verified that : 

Area of a rhombus =1/2 x product of its diagonals.

 Class 08 Activity – Surface Area of a cube and cuboid

Objective: 

To verify the formula for surface area of a cube and a cuboid. Or to verify the following formulae

Surface area of a cube = 6 (side)2.

Surface area of a cuboid= 2 (length x breadth + breadth x height + height x length)

Materials Required: 

Thick sheets of paper, a pair of scissors, sello tape, geometry box, etc.

procedure: 

(a) Cube:

On a thick sheet of paper, draw a net of a cube., as shown below. It consists of six identical squares. Using a pair of scissors, cut it out.

2. Fold the net along the dotted lines and use sellotape to get a cuboid of 

edge 3 cm.

(b) Cuboid:

On a thick sheet of paper, draw the net of a cuboid as shown below. It consists of 6 rectangles. Using a pair of scissors cut it out.

2. Fold the net and use sellotape to form a cuboid of dimensions 

5 cm x 4 cm x 2 cm.

Observations:

Surface area of the cube obtained in figure 2 is equal to the sum of the areas of all the six squares in fig. 

Side of each square = 3 cm

So, area of 1 square = 32 sq cm.

 Area of 6 squares = 6 x 32 sq cm.

Or surface area of the cube in fig = 6 x 32 sq.cm. 

= 6 x (edge)2  sq. units.

2. Surface area of the cuboid in figure is equal to the sum of the areas of all the six rectangles in fig. Figure consists of :

2 rectangles of dimensions 5 cm x 4 cm.

2 rectangles of dimensions 4 cm x 2 cm and

2 rectangles of dimensions 2 cm x 5 cm.

So, sum of the areas of all the rectangles in figure 

= [2 (5 x 4) + 2 (4 x 2) + (2 x 5)] sq cm.

= 2 [(5 x 4) + (4 x 2) + (2 x 5)] sq cm.

Or surface area of the cuboid in figure 

= 2 [(5 x 4) + (4 x 2) + (2 x 5)] sq cm.

= 2 [length x breadth + breadth x height + height x length] sq units.

Conclusion : 

From the above activity, it is verified that : 

Total surface area of a cube = 6(edge)2

(b) Total surface area of a cuboid 

= 2 [length x breadth + breadth x height + height x length] sq units.

 Class 08 Activity – Area of Trapezium

Objective: 

To verify the formula for area of a trapezium. Or to verify the following formula Area of a trapezium = 1/2 sum of the parallel sides x distance between them.

Materials Required: 

Squared paper, a pair of scissors, colour pencils, geometry box, etc.

Procedure: 

1. On a squared paper, draw a trapezium ABCD in which AB || CD and AB = 8 cm, CD = 4 cm and distance between them is 5 cm. 

Using a pair of scissors, cut it out. Colour it green. 

2. On another squared sheet draw one more copy of the parallelogram ABCD. Cut it out and colour it red.

3. Take a white sheet of paper and paste the green coloured trapezium ABCD on it. Paste the red coloured trapezium ABCD next to the green coloured trapezium such that A falls at D and AD falls along DA as shown below.

Observations:

In figure, we observe that the resulting shape is a parallelogram as its one pair of opposite sides is parallel and equal, each equal to (8 + 4) cm.

2. The parallelogram in figure is made up of two congruent trapeziums ABCD.

So, area of trapezium ABCD 

= 1/2 x area of parallelogram in figure 

= 1/2x base x height

= 1/2 x (8 + 4) x 5 cm

= 1/2 x sum of parallel sides x distance between them.

Conclusion: 

From the above activity, it is verified that:

Area of a trapezium = 1/2 x sum of parallel sides x distance between them.

Do Yourself: Verify the formula for area of a trapezium by drawing three different trapeziums on squared papers.

 Based on CHAPTERs10. Visualizing Solid shapes11. Mensuration5. Data Handling15. Introduction to Graphs

Class 08 Activity – Volumes and Surface Areas

Objective: 

To explore the relationship between

(i)  length (in cm ) and perimeter (in cm)

(ii) length (in cm) and area (in cm²) 

Of 5 squares of different dimensions drawn on a squared paper.

Materials Required:  

Squared paper, colour pencils, geometry box,  etc.

Procedure 

On a squared paper, draw five squares of different dimensions. Name these squares as1 2 3 4 5. 

Now, measure the perimeter of each square. Also, count the number of small squares (the area of each small square being 1 cm²) enclosed by each square to get their areas. 

Complete the following table.

Observations:

 From the table, we observe that:

Perimeter of a square is four times its length. Or side of a square is one fourth of its perimeter. 

So, for а square,  "Perimeter" /"Length" =4. 

2. Area of a square of length l is l x l = l ². Or side of a square of area A square units is √A units.

 So, for a square, "Area" /"Length" = Length

Conclusion: 

From the above activity, we observe that for a square of length l :

Perimeter = 4 x l 

2. Area = l x l = l ² 

Do Yourself: On a squared paper, draw four different squares and explore the relationship between:

1. length and perimeter

2. length and area.