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

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

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15 Jun 2016, 01:10
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58% (01:04) correct 42% (00:43) wrong based on 732 sessions

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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$$\pi$$
[Reveal] Spoiler: OA

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Md. Abdur Rakib

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Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

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

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18 Jun 2016, 04:36
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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$$\pi$$

Let the height of the semi-circle be x. The height is same as the radius of the semi-circle.

Now consider the height of the rectangle as 10-x.

Given diameter of the circle is 4 and we get the radius as 2.

=> We get the height of the rectangle as 10-2 = 8. Now the area of the rectangle is 8 * 4 = 32.

The area of the semi circle is $$\pi$$ * r^2 / 2.
=> $$\pi$$ * 4 / 2 => $$\pi$$ * 2 ( or ) 2$$\pi$$.

Finally the sum of the areas of rectangle + semi circle is 32 + 2$$\pi$$.
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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

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18 Jun 2016, 05:04
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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$$\pi$$

Attachment:

vaxpj.jpg [ 33.73 KiB | Viewed 5312 times ]

Since the top part is a Semicircle , its area will be$$\frac{1}{2}$$*$$\pi$$ *$$2^2$$ = 2$$\pi$$

Area of the rectangle will be 8*4 =32

So, Total area is 32+ 2$$\pi$$

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

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19 Jun 2016, 01:09
How do you guys type pi?

The rectangle is 32, and the semi-circle is half of 4pi. So the answer is 32 + 2pi.

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

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19 Jun 2016, 02:17
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Expert's post
HiLine wrote:
How do you guys type pi?

The rectangle is 32, and the semi-circle is half of 4pi. So the answer is 32 + 2pi.

$$\pi$$: write \pi, mark and press m button.

Hope it helps.
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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, 03:05
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 = $$32 + 2\pi$$

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, 03:37, edited 1 time in total.

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

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02 Aug 2016, 14:04
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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.

Shortcut method:

Conventional method:

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

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16 Sep 2016, 23:00
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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

So by elimination the answer is E

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

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16 Sep 2016, 23:54
area of semicircle = 2πr/2 = 2π
height of semi circle = 2
so l=8 b=4
lb = 32
window = 32 + 2π

E

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

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11 Oct 2016, 01:28
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.

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

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05 Aug 2017, 04:23
Estimate Shortcut:

If it were a rectangle of 4 x 10 then the area would be 40. But we chip of some area to make it a semicircle. Thus actual area is less than 40.

Pi = 3 (approx)

All answers except E are bigger than 40, we need something smaller than 40

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The window in the figure above consists of a rectangle and a semicircl   [#permalink] 05 Aug 2017, 04:23
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