Question

Find the area of the entire figure.

Answer 1

`\large\boxed{A=171.555\ in^2}`

Explanation:

We have the right triangle and the trapezoid.

The formula of an area of a right triangle:

`A_(triangle)=(ab)/(2)`

a, b - legs

We have the length of the legs 12in and 13.42 in. Substitute:

`A_(triangle)=((12)(13.42))/(2)=80.52\ in^2`

The formula of an area of a trapezoid:

`A_(trapezoid)=((b_1+b_2)h)/(2)`

b₁, b₂ - bases

h - height

We have the length of the bases 18in and 11.75in and the length of the height 6.12in. Substitute:

`A_(trapezoid)=((18+11.75)(6.12))/(2)=((29.75)(6.12))/(2)=91.035\ in^2`

The area of the figure:

`A=A_(triangle)+A_(trapezoid)`

Substitute:

`A=80.52+91.035=171.555\ in^2`