Answer:
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 = [tex]\frac{1}{4} \pi r^{2}[/tex]
Also,
We know that ,
Area of isosceles Triangle = [tex]\frac{1}{2}*Base*Height[/tex]
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 = [tex]\frac{1}{4} \pi (8)^{2}[/tex] = 16[tex]\pi[/tex]
Area of isosceles Triangle = [tex]\frac{1}{2}*8*8[/tex] = 32
Now,
Area of Shaded area = Area of a quarter circle - Area of isosceles Triangle
= 16[tex]\pi[/tex] - 32
= 50.265 - 32
= 18.265 ≈ 18.3
⇒Area of Shaded Area = 18.3
