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If each curved side in the figure above is a semicircle with [#permalink]
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Expert's post 00:00

Question Stats: 81% (01:00) correct 18% (00:42) wrong based on 53 sessions
Attachment: semi.jpg [ 30.65 KiB | Viewed 1767 times ]

If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the shaded region?

(A) $$2,000$$

(B) $$4,000$$

(C) $$2,000 - 200\pi$$

(D) $$4,000 - 200\pi$$

(E) $$4,000 - 400\pi$$
[Reveal] Spoiler: OA

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Re: If each curved side in the figure above is a semicircle with [#permalink]
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Carcass wrote:
Attachment:
The attachment semi.jpg is no longer available

If each curved side in the figure above is a semicircle with radius 20, and the two parallel sides each have length 100, what is the area of the shaded region?

(A) $$2,000$$

(B) $$4,000$$

(C) $$2,000 - 200\pi$$

(D) $$4,000 - 200\pi$$

(E) $$4,000 - 400\pi$$

Here,
Let us calculate the whole figure as one with 2 semicircle(1 shaded in red and other in black) and 1 rectangle (Please refer to the picture attached) and then after calculating the area's of each one of them we can deduct the semicircle (shaded in red)which will left us with the area of the shaded region
First let us calculate the area of the semicircle = $$\pi r^2$$/2

therefore the area of the semicircle down =$$200\pi$$ and the semicircle of the top (red shaded) =$$200\pi$$

and the area of the circle

Now the area of the rectangle (including the semicircle red shaded)= L *B

we know Length = 100

Therefore the area = 100 * 40 = 4000

Now the area of the shaded region only= 4000 + $$200\pi$$(semi circle shaded in black) -$$200\pi$$(semi circle shaded in red) = 4000
Attachments Untitled.png [ 55.32 KiB | Viewed 1727 times ]

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Re: If each curved side in the figure above is a semicircle with [#permalink]
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No need to do hard calculation. Just Place the lower portion on the upper side. Then it becomes a complete rectangle.

Here, radius = 20, so diameter = 40 which is the width or other side of the rectangle. On the other hand the parallel side = 100.

Then, area of the rectangle = 40 X 100 = 4000.

Ans: B
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Re: If each curved side in the figure above is a semicircle with [#permalink]
There is confusion in the picture. The upper semi circle is missing? We have to calculate the area of missing semi circle? or the rectangular body + lower semi circle? As per replies given above, i am confused about the given picture
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Re: If each curved side in the figure above is a semicircle with [#permalink]
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Expert's post
Farina wrote:
There is confusion in the picture. The upper semi circle is missing? We have to calculate the area of missing semi circle? or the rectangular body + lower semi circle? As per replies given above, i am confused about the given picture Since the red semicircle and the green semicircle both have the same radii, we know that they both have the same area.
So if we move the red semicircle into the empty semicircle-shaped space at the top, we get a nice rectangle.

Does that help?
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Re: If each curved side in the figure above is a semicircle with [#permalink]
GreenlightTestPrep wrote:
Farina wrote:
There is confusion in the picture. The upper semi circle is missing? We have to calculate the area of missing semi circle? or the rectangular body + lower semi circle? As per replies given above, i am confused about the given picture Since the red semicircle and the green semicircle both have the same radii, we know that they both have the same area.
So if we move the red semicircle into the empty semicircle-shaped space at the top, we get a nice rectangle.

Does that help?

Hi Brent, thanks for your reply. So we have to find the area of one semicircle and the rectangle right?
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Re: If each curved side in the figure above is a semicircle with [#permalink]
Expert's post
Farina wrote:
There is confusion in the picture. The upper semi circle is missing? We have to calculate the area of missing semi circle? or the rectangular body + lower semi circle? As per replies given above, i am confused about the given picture

This is the way GRE tests your critical skill.

rest for sure the geometry figure is correct.

Regards
_________________ Re: If each curved side in the figure above is a semicircle with   [#permalink] 06 May 2020, 10:52
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