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what is the area of the square?

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by BTGmoderatorLU » Sat Nov 11, 2017 8:18 am
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In the figure above the square has two sides which are tangent to the circle, If the area of the circle is 4a²π, what is the area of the square?

A. 2a²
B. 4a
C. 4a²
D. 16a²
E. 64a²

The OA is D.

Experts, I need your help with this PS question, I don't have it clear. Please, can you explain it for me? Thanks.
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by Brent@GMATPrepNow » Sat Nov 11, 2017 8:48 am
LUANDATO wrote:Image

In the figure above the square has two sides which are tangent to the circle, If the area of the circle is 4a²π, what is the area of the square?

A. 2a²
B. 4a
C. 4a²
D. 16a²
E. 64a²

The OA is D.

Experts, I need your help with this PS question, I don't have it clear. Please, can you explain it for me? Thanks.
The area of the circle is 4a²π
Area of circle = π(radius)²
= 4a²π
= π4a²
= π(2a)²
So, the radius = 2a
This means the diameter = 4a (diameter is TWICE the radius)

What is the area of the square?
Each side of the square has length 4a
Area of square = side²
= (4a )²
= 16a²
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Sat Oct 26, 2019 7:40 am
BTGmoderatorLU wrote:Image

In the figure above the square has two sides which are tangent to the circle, If the area of the circle is 4a²π, what is the area of the square?

A. 2a²
B. 4a
C. 4a²
D. 16a²
E. 64a²

The OA is D.

Experts, I need your help with this PS question, I don't have it clear. Please, can you explain it for me? Thanks.
We see that the radius of the circle is 2a, so a side of the square is 4a, and thus, the area of the square is (4a)^2 = 16a^2.

Answer: D

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