Question

What is the area of this composite shape?

Enter your answer in the box.

_in²

Answer 1

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

Step-by-step 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* width`

where
`length = 5` and
`width = 5`

Substituting, we have,

`A_1=7* 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=(1)/(2) bh`

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

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

Substituting, we have,

`A_2=(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`