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The window in the figure above consists of a rectangle and a semicircl [#permalink]

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19 Jun 2016, 04:05

Area of the semicircle = \(\frac{\pi r^2}{2}\) Since Radius is 2 therefore Area of the semicircle =>\(\frac{\pi*2*2}{2}\)===> \(2\pi\) Area of the rectangle=\(l . b = 8 x 4 = 32\)

total area = \(32 + 2\pi\) Answer is E

AbdurRakib wrote:

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\) B) 40 + 2\(\pi\) C) 32 + 8\(\pi\) D) 32 + 4\(\pi\) E) 32 + 2\(\pi\)

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Last edited by LogicGuru1 on 17 Sep 2016, 04:37, edited 1 time in total.

Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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02 Aug 2016, 15:04

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Here are a couple of videos about this problem. The first goes over a shortcut method to solve the question in a few seconds. The second goes over a more conventional, but more versatile, approach.

Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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17 Sep 2016, 00:00

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I see this differently. If this was purely a rectangle, then the area would be 40sq.f

So A and B are automatically wrong. Say I don't remember my geometry and only know that pi is 3.14, then everything is easy. C=32+8*3.14=too much D=32+4*3.14=too much

Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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11 Oct 2016, 02:28

lololol650 wrote:

I see this differently. If this was purely a rectangle, then the area would be 40sq.f

So A and B are automatically wrong. Say I don't remember my geometry and only know that pi is 3.14, then everything is easy. C=32+8*3.14=too much D=32+4*3.14=too much

So by elimination the answer is E

Did it the same way.

Half-circle --> 2/pi, we can narrow down the choices to two. If it would be a full rectangle --> 4 * 10 = 40. But it is not a full rectangle. --> Must be E.

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8\(\pi\) B) 40 + 2\(\pi\) C) 32 + 8\(\pi\) D) 32 + 4\(\pi\) E) 32 + 2\(\pi\)

We are given a semicircle with a diameter of 4 ft., which also represents the width of the rectangle. We are also given that height of the window is 10 ft., which is the combined length of the radius of the semicircle and the length of the rectangle. To determine the length of the rectangle, we can subtract the radius of the semicircle, which is 2 ft., from the total length of 10 ft.:

10 - 2 = 8 ft.

Now we can calculate the area of the semicircle and the rectangle.

Area of semicircle = (1/2)π(2^2) = 2π

Area of rectangle = 8 x 4 = 32

Thus, the total area is 32 + 2π.

Answer: E
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