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.