Question

21. A Figure is shown below.
What is the area of the figure, in square inches?

Answer 1

Answer: 36+27in2

Explanation:

Answer 2

`36+27\pi\:\mathrm{in^2}`

Explanation:

The figure consists of a square and a sector. We can add the areas of the square and sector to get the total area of the figure.

The area of a sector with measure
`\theta` in a circle of radius
`r` is equal to
`(\theta)/(360)\cdot r^2\pi`. Since there are 360 degrees in a circle and 90 degrees in each corner of a square, the measure of the sector is
`270^(\circ)`.

Thus, its area is:

`(270)/(360)\cdot6^2\cdot pi=(3)/(4)\cdot 6^2\cdot \pi=27\pi`.

The area of a square with side length
`s` is given by
`s^2`. Therefore, the area of the circle is
`6^2=36` and the total area of the figure is
`\boxed{36+27\pi\:\mathrm{in^2}}`