Question

There is a pentagonal shaped parts as shown in figure. For finding its area Jyothi and Rashida divided it in two different ways. Find the area in both ways and what do you observe?

Answer 1

Jyoti : The area of ABCDE = 2 $\times$ ar. trap. MBCD

= $2\times \frac{1}{2}(DM+CB)\times MB$

= $(30+15)\times 7.5=337.5{cm}^2$

Rashido : The area of ABCDE = ar ABCE + ar $△$EDC

= $(15\times 15)+\frac{1}{2}\times 15\times 15$

= 225 + 112.5 = 337.5${cm}^2$

The area of both the cases is same.