Question

In the following diagram, a quarter circle has been constructed using an isosceles right triangle whose legs measure 8 inches. Which of the following represents the area of the shaded region, rounded to the nearest tenth of a square inch?

Answer 1

Area of Shaded Area = 18.3

Explanation:

P.S - The exact question is -

Given - In the following diagram, a quarter circle has been constructed using an isosceles right triangle whose legs measure 8 inches.

To find - Which of the following represents the area of the shaded region, rounded to the nearest tenth of a square inch?

Proof -

We know that,

Area of a quarter circle =
`(1)/(4) \pi r^(2)`

Also,

We know that ,

Area of isosceles Triangle =
`(1)/(2)*Base*Height`

Now,

Given that,

Radius of quarter circle = 8 inches

Base of Isosceles Triangle = 8 inches

Height of Isosceles Triangle = 8 inches

∴ we get

Area of a quarter circle =
`(1)/(4) \pi (8)^(2)` = 16
`\pi`

Area of isosceles Triangle =
`(1)/(2)*8*8` = 32

Now,

Area of Shaded area = Area of a quarter circle - Area of isosceles Triangle

= 16
`\pi` - 32

= 50.265 - 32

= 18.265 ≈ 18.3

⇒Area of Shaded Area = 18.3