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# In the square above, what is the area of the shaded region?

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
In the square above, what is the area of the shaded region?  [#permalink]

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11 Oct 2017, 00:58
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Difficulty:

5% (low)

Question Stats:

94% (01:06) correct 6% (00:58) wrong based on 79 sessions

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In the square above, what is the area of the shaded region?

(A) 11/10
(B) 4/5
(C) 7/10
(D) 3/5
(E) 2/5

Attachment:

2017-10-11_1156.png [ 8.22 KiB | Viewed 1309 times ]

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Re: In the square above, what is the area of the shaded region?  [#permalink]

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11 Oct 2017, 01:55
1/4*1/5*14=7/10

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In the square above, what is the area of the shaded region?  [#permalink]

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11 Oct 2017, 08:13
Bunuel wrote:

In the square above, what is the area of the shaded region?

(A) 11/10
(B) 4/5
(C) 7/10
(D) 3/5
(E) 2/5

Attachment:
2017-10-11_1156.png

The area of one small square is $$\frac{1}{4}$$ * $$\frac{1}{5}$$ = $$\frac{1}{20}$$

There are 5 * 4 = 20 small squares

6 of 20 are not shaded. 14 of 20 are. Area of shaded region:

$$\frac{1}{20}$$ * 14 = $$\frac{14}{20}$$ = $$\frac{7}{10}$$

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Re: In the square above, what is the area of the shaded region?  [#permalink]

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11 Oct 2017, 08:22
Total area = 1/4 * 4 * 1/5 * 5 = 1

Shaded area = 1 - (1*1/5 + 1/4*2/5) = 7/10
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Re: In the square above, what is the area of the shaded region?  [#permalink]

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12 Oct 2017, 07:23
Bunuel wrote:

In the square above, what is the area of the shaded region?

(A) 11/10
(B) 4/5
(C) 7/10
(D) 3/5
(E) 2/5

Attachment:
2017-10-11_1156.png

Number of shaded box to Total number of boxes

14/20 equals to 7/10
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Re: In the square above, what is the area of the shaded region?  [#permalink]

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13 Oct 2017, 09:26
Bunuel wrote:

In the square above, what is the area of the shaded region?

(A) 11/10
(B) 4/5
(C) 7/10
(D) 3/5
(E) 2/5

Attachment:
2017-10-11_1156.png

Since each small shaded rectangle has area (1/5)(1/4) = 1/20 and there are 14 such rectangles, the total area of the shaded region is 14 x 1/20 = 14/20 = 7/10.

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Re: In the square above, what is the area of the shaded region?  [#permalink]

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15 Oct 2017, 06:56
Number of shaded squares = 14
Area of each shaded square = 1/4 * 1/5 = 1/20
So area of shaded region = 1/20 * 14 = 7/10

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Re: In the square above, what is the area of the shaded region?  [#permalink]

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22 Nov 2017, 18:43
The quicker method is to count the number of shaded boxes and determine the area based on fractions.

There are 14 shaded boxes and 6 unshaded boxes. Therefore, area of the shaded boxes is 14/20 = 7/10.

Another method is to calculate the area.
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Re: In the square above, what is the area of the shaded region? &nbs [#permalink] 22 Nov 2017, 18:43
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