Question

Find the area of the figure. Round to the hundredth place when necessary.​

Answer 1

`Area =155 \: yd^(2)`

Explanation:

We have to cut this figure into several other figures, refer to the attached diagram where I have shown that the given figure can be cut into 3 different figures;

1. Rectangle

2. Triangle

3. Parallelogram

So we are going to find the area of these 3 shapes then we will add them together that will give us the area of whole figure.

Area of Rectangle:

The area of rectangle is given by

`A_(rectangle) = w\cdot l`

`w = 3 \: yd`

`l = 8 \: yd`

`A_(rectangle) = 3\cdot 8 = 24 \: yd^(2)`

Area of Parallelogram:

The area of parallelogram is given by

`A_(parallelogram) = b\cdot h`

`b = 13 \: yd`

`h = 15 - 8 = 7 \: yd`

`A_(parallelogram) = 13\cdot 7 = 91 \: yd^(2)`

Area of Triangle:

The area of triangle is given by

`A_(triangle) = (1)/(2)\cdot b\cdot h`

`b = 13 - 3 = 10 \: yd`

`h = 8 \: yd`

`A_(triangle) = (1)/(2)\cdot 10\cdot 8=40 \: yd^(2)`

Area of whole figure:

`Area = A_(rectangle) + A_(parallelogram) + A_(triangle)`

`Area = 24 + 91 + 40`

`Area =155 \: yd^(2)`

Therefore, the area of the whole figure is 155 square yd.