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## Find the area of the shaded region.

tagged by: AAPL

This topic has 2 expert replies and 0 member replies

### Top Member

AAPL Master | Next Rank: 500 Posts
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#### Find the area of the shaded region.

Mon Feb 26, 2018 2:56 pm

In the figure above, AC = BC = 8, angle C = 90Â°, and the circular arc has its center at point C. Find the area of the shaded region.

$$A.\ 8\pi-32$$
$$B.\ 16\pi-32$$
$$C.\ 16\pi-64$$
$$D.\ 32\pi-32$$
$$E.\ 32\pi-64$$

The OA is B.

In this PS question, I just need to find the area of the circular arc and then subtract the area of the triangle, right?

It will be,
$$A_{ARC}-A_{\triangle}=\frac{1}{2}r^2\theta-\frac{1}{2}b\cdot h=\frac{1}{2}8^2\frac{\pi}{2}-\frac{1}{2}8\cdot8=16\pi-32$$

Is there a strategic approach to this question? Can any experts help me, please?

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
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Posted:
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Upvotes:
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Wed Feb 28, 2018 10:32 am
AAPL wrote:

In the figure above, AC = BC = 8, angle C = 90Â°, and the circular arc has its center at point C. Find the area of the shaded region.

$$A.\ 8\pi-32$$
$$B.\ 16\pi-32$$
$$C.\ 16\pi-64$$
$$D.\ 32\pi-32$$
$$E.\ 32\pi-64$$
We see that the radius of the quarter circle is 8, so the area of the quarter circle is:

1/4 x 8^2 x Ï€ = 16Ï€

The area of the triangle is 8 x 8 x 1/2 = 32

Thus, the area of the shaded region is 16Ï€ - 32.

Answer: B

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
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1229 members
Upvotes:
5254
GMAT Score:
770
Tue Feb 27, 2018 9:21 am
AAPL wrote:

In the figure above, AC = BC = 8, angle C = 90Â°, and the circular arc has its center at point C. Find the area of the shaded region.

$$A.\ 8\pi-32$$
$$B.\ 16\pi-32$$
$$C.\ 16\pi-64$$
$$D.\ 32\pi-32$$
$$E.\ 32\pi-64$$

Area of shaded region = (area of sector) - (area of triangle)

Area of circle = Ï€(radius)Â²
Area of triangle = (base)(height)/2

The sector ABC is 1/4 of a circle of radius 8
So, area of sector = (1/4)(Ï€)(8Â²)
= 16Ï€

area of triangle = (8)(8)/2
= 32

So, area of shaded region = (16Ï€) - (32)

Answer: B

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
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