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A triangle is inside a circle where the triangle's base is on the circle's diameter as shown.

What is the area of the shaded region?

Use 3.14 for π .

Enter your answer as a decimal in the box.

A triangle is inside a circle where the triangle's base is on the circle's diameter-example-1

2 Answers

4 votes
area of a circle=pi x r^2= 3.14 x 8^2(half of the radius)=3.14 x 64=200.96

area of triangle= 1/2 bh=1/2(16)(8)=1/2(128)=64

200.96-64=136.96 sq.ft
User TomSjogren
by
8.5k points
7 votes

Answer:


A_(shaded)= 136.96 ft^(2)

Explanation:

We will find the shaded area if we subtract the area of the triangle from the area of the circle.

We know that the area of the circle is defined as


A= \pi r^(2)

Where
r is half the diameter, that is


r=(16ft)/(2)=8ft

The area of the circle is


A= \pi r^(2)\\A= 3.14 (8ft)^(2) =200.96ft^(2)

Now, we have to find the area of the triangle, which is defined as


A_(\triangle) =(bh)/(2)

Where
b is the base of 16 feet, and
h is the height of the triangle which is on the radius. So, we have
b=16ft and
h=8ft.

The area of the triangle is


A_(\triangle) =(16ft(8ft))/(2)=64ft^(2)

Now, the shaded is the difference as we said before, that is


A_(shaded)=A-A_(\triangle)

Replacing both areas, we have


A_(shaded)=200.96 ft^(2) - 64ft^(2)= 136.96 ft^(2)

Therefore, the shaded area is
A_(shaded)= 136.96 ft^(2)

User Newton Joshua
by
9.0k points

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