Question

The polygons are similar. The area of one polygon is given. Find the areas of the other polygon.

Answer 1

`Area = 6cm^2`

Explanation:

Given

See attachment for polygons

Required

The area of the other polygon

From the attachment, we have:

`A_1= 96cm^2`

`b_1= 12cm`

and

`b_2= 3cm`

In
`A_1= 96cm^2` and
`b_1= 12cm`

The area is calculated as:

`Area = 0.5 * base * height`

`A_1 = 0.5 * b_1 * h_1`

`96 = 0.5 * 12 * h_1`

`96 = 6 * h_1`

Solve for h

`h_1 = 16`

Next, is to calculate the height of the other polygon using the following equivalent ratios;

`b_1 : h_1 = b_2 : h_2`

This gives:

`12 : 16 = 3 : h_2`

As fraction

`(12 )/( 16 )= (3 )/( h_2)`

Solve for h

`h_2 = (16 * 3)/(12)`

`h_2 = 4`

So, the area is

`Area = 0.5 * base * height`

`Area = 0.5 * b_1 * h_1`

`Area = 0.5 * 3 * 4`

`Area = 6cm^2`