The window in the figure above consists of a rectangle and a semicircl : Problem Solving (PS)

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AbdurRakib

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

15 Jun 2016, 02:10

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A

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C

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E

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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) \(32 + 2\pi\)

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GMATAcademy

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

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.

Shortcut method:

Conventional method:

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msk0657

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

18 Jun 2016, 05:36

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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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Abhishek009

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

18 Jun 2016, 06:04

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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 54342 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\(\pi\)

Answer will be (E)
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HiLine

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

19 Jun 2016, 02:09

How do you guys type pi? :shock:

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

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Bunuel

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

19 Jun 2016, 03:17

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HiLine wrote:

How do you guys type pi? :shock:

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.

Check for more here: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

Hope it helps.
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LogicGuru1

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

Updated on: 17 Sep 2016, 04:37

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\(\pi\)

Originally posted by LogicGuru1 on 19 Jun 2016, 04:05.
Last edited by LogicGuru1 on 17 Sep 2016, 04:37, edited 1 time in total.

lololol650

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

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

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]

17 Sep 2016, 00:54

area of semicircle = 2πr/2 = 2π
height of semi circle = 2
so l=8 b=4
lb = 32
window = 32 + 2π

E

AK125

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

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.

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mevicks

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

05 Aug 2017, 05:23

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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ScottTargetTestPrep

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

19 Dec 2017, 07:42

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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\(\pi\)

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

03 Jul 2020, 07:39

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 need understand that the figure is composed of a semicircle and a rectangle.

Area of the semicircle would be pi*radius^2/2=2 pi

We need to next find the area of the rectangle, the radius of circle will be 2 all throughout therefore we can find the length of the rectangle, which is 10-2=8.

Area of rectangle =8*4=32

Area of the figure = \(32 + 2\pi\) . E
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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

30 May 2021, 07:15

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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) \(32 + 2\pi\)

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PS13827_f001.png

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BrentGMATPrepNow

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

Updated on: 03 Apr 2022, 09:18

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Top Contributor

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) \(32 + 2\pi\)

Show Spoiler

Attachment:

PS13827_f001.png

GMAT STRATEGY: While it's perfectly natural to attempt to solve the question "mathematically" (by applying various formulas), you should have an alternate plan if you're unable to answer the question. In this case, you might be able to apply the fact that the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise.
I can see that, if we (mentally) draw a rectangle around the diagram, we get something like this:

Since the dimensions of the rectangle are 4 feet by 10 feet, the area of the rectangle = (base)(height) = (4)(10) = 40 square feet, which means the area of the original diagram must be a little bit less than 40 square feet.

When we check the options, we see that answer choices A, B, C and D are all greater than 40.
So, the correct answer must be E.

Originally posted by BrentGMATPrepNow on 23 Mar 2022, 15:40.
Last edited by BrentGMATPrepNow on 03 Apr 2022, 09:18, edited 1 time in total.

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

29 Mar 2022, 17:19

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Video solution from Quant Reasoning:
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Re: The window in the figure above consists of a rectangle and a semicircl [#permalink]

22 Jul 2023, 02:00

Area of window = area of rectangle + area of semi circle
= 4x8 + 1/2xπx(2)^2
= 32 + 2π

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Paras96

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

24 Jul 2023, 01:01

Area of window = Area of semicircle + area of rectangle = (π(2)^2)/2 + 4*(10-2)=2π+32

Hence E

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chloe2m

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

13 Jan 2024, 09:29

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) \(32 + 2\pi\)

Show Spoiler

Attachment:

PS13827_f001.png

Please correct me if I am wrong but if you want to solve this in less than 15 seconds ;
Observe that the area has to be less than 4 x 10 : 40 (if the window was a full rectangle). This clearly eliminates answer A and B. Knowing that pi is almost 3,14 you can thus observe that C and D will also be above 40.
Thus only answer possible is E.

gmatclubot

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

13 Jan 2024, 09:29

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