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# In the figure, ABCD is a rectangle. What is the area of the shaded reg

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Math Expert
Joined: 02 Sep 2009
Posts: 54410
In the figure, ABCD is a rectangle. What is the area of the shaded reg  [#permalink]

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05 Apr 2019, 01:38
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Difficulty:

25% (medium)

Question Stats:

71% (01:17) correct 29% (01:47) wrong based on 28 sessions

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In the figure, ABCD is a rectangle. What is the area of the shaded region in the figure?

(A) 18
(B) 20
(C) 24
(D) 28
(E) 32

Attachment:

2019-04-05_1237.png [ 81.26 KiB | Viewed 465 times ]

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Re: In the figure, ABCD is a rectangle. What is the area of the shaded reg  [#permalink]

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05 Apr 2019, 02:50
Bunuel wrote:

In the figure, ABCD is a rectangle. What is the area of the shaded region in the figure?

(A) 18
(B) 20
(C) 24
(D) 28
(E) 32

Attachment:
2019-04-05_1237.png

Area of the shaded region=Area of rectangle-(Area of right angle triangle AEF+ Area of triangle DCB)
$$=12*7-(\frac{1}{2}*7*12+\frac{1}{2}*6*8)=18$$

Ans. (A)
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Re: In the figure, ABCD is a rectangle. What is the area of the shaded reg  [#permalink]

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05 Apr 2019, 03:54
Bunuel wrote:

In the figure, ABCD is a rectangle. What is the area of the shaded region in the figure?

(A) 18
(B) 20
(C) 24
(D) 28
(E) 32

Attachment:
2019-04-05_1237.png

area of rectangle - area of ∆
84-(1/2* 8*6+1/2*7*6)
IMO A
; 18
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Re: In the figure, ABCD is a rectangle. What is the area of the shaded reg  [#permalink]

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06 Apr 2019, 19:05
Bunuel wrote:

In the figure, ABCD is a rectangle. What is the area of the shaded region in the figure?

(A) 18
(B) 20
(C) 24
(D) 28
(E) 32

Attachment:
2019-04-05_1237.png

Area of half the rectangle=$$\frac{1}{2}*(6+1)*(8+4)=42$$

Area of shaded region=$$42-\frac{1}{2}*6*8=18.$$

IMO, Option A.
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Re: In the figure, ABCD is a rectangle. What is the area of the shaded reg   [#permalink] 06 Apr 2019, 19:05
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# In the figure, ABCD is a rectangle. What is the area of the shaded reg

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