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?

Area of Shaded Area = 18.3

Step-by-step 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 =

Also,

We know that ,

Area of isosceles Triangle =

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 = = 16

Area of isosceles Triangle = = 32

Now,

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

                                 = 16 - 32

                                 = 50.265 - 32

                                 = 18.265 ≈ 18.3

⇒Area of Shaded Area = 18.3

step-by-step explanation: