Question

Find the area of the similar
figure.
20cm
25cm
Area = 320cm2 Area = [?]cm2

Answer 1

Given:

Base of smaller figure = 20 cm

Area of smaller figure = 320 cm²

Base of the larger figure = 25 cm

To find:

The area of the larger figure.

Solution:

We know that the areas of the similar figure are proportional to the square of corresponding sides of them.

Let A be the area of the larger figure.

`\frac{\text{Area of the larger figure}}{\text{Area of the smaller figure}}=\frac{(\text{Base of the larger figure})^2}{(\text{Base of the smaller figure})^2}`

`(A)/(320)=((25)^2)/((20)^2)`

`(A)/(320)=(625)/(400)`

`(A)/(320)=(25)/(16)`

Multiply both sides by 320.

`A=(25)/(16)* 320`

`A=500`

Therefore, the area of the larger figure is 500 cm².