Answer:
[tex]Area = 6cm^2[/tex]
Step-by-step explanation:
Given
See attachment for polygons
Required
The area of the other polygon
From the attachment, we have:
[tex]A_1= 96cm^2[/tex]
[tex]b_1= 12cm[/tex]
and
[tex]b_2= 3cm[/tex]
In [tex]A_1= 96cm^2[/tex] and [tex]b_1= 12cm[/tex]
The area is calculated as:
[tex]Area = 0.5 * base * height[/tex]
[tex]A_1 = 0.5 * b_1 * h_1[/tex]
[tex]96 = 0.5 * 12 * h_1[/tex]
[tex]96 = 6 * h_1[/tex]
Solve for h
[tex]h_1 = 16[/tex]
Next, is to calculate the height of the other polygon using the following equivalent ratios;
[tex]b_1 : h_1 = b_2 : h_2[/tex]
This gives:
[tex]12 : 16 = 3 : h_2[/tex]
As fraction
[tex]\frac{12 }{ 16 }= \frac{3 }{ h_2}[/tex]
Solve for h
[tex]h_2 = \frac{16 * 3}{12}[/tex]
[tex]h_2 = 4[/tex]
So, the area is
[tex]Area = 0.5 * base * height[/tex]
[tex]Area = 0.5 * b_1 * h_1[/tex]
[tex]Area = 0.5 * 3 * 4[/tex]
[tex]Area = 6cm^2[/tex]
