Question

What is the area of this composite shape?


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_in²

Answer 1

The area of the composite figure is $40 in^2$

Explanation:

From the given figure, we can see that the area of the composite figure = area of the rectangle + area of the triangle.

Area of the rectangle $(A_1)$:

The formula is given by

$A_1=length\times width$

where $length = 5$ and $width = 5$

Substituting, we have,

$A_1=7\times 5=35 in^{2}$

Thus, the area of the rectangle = $35 i n^{2}$

Area of the triangle $(A_2)$:

The formula is given by

$A_2=\frac{1}{2} bh$

where $b=5-3=2 i n$

and $h=12-7=5 \text { in }$

Substituting, we have,

$A_2=\frac{1}{2} (2)(5)\\A_2=5 in ^{2}$

Thus, the area of the triangle = $5in ^{2}$

Area of the composite figure = Area of the rectangle + area of the triangle

Area of the composite figure = $35 i n^{2}+5 i n^{2}=40 i n^{2}$

Thus, the area of the composite figure is $40 in^2$