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# ABCD and EFGH are rectangles. What is the area of the shaded region?

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Math Expert
Joined: 02 Sep 2009
Posts: 51135
ABCD and EFGH are rectangles. What is the area of the shaded region?  [#permalink]

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26 Jun 2018, 20:07
00:00

Difficulty:

5% (low)

Question Stats:

97% (00:31) correct 3% (00:00) wrong based on 41 sessions

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ABCD and EFGH are rectangles. What is the area of the shaded region?

A. $$3x^2 — xy$$

B. $$4x^2 — xy$$

C. $$4x^2 — 2xy$$

D. $$6x^2 — xy$$

E. $$6x^2 — 2xy$$

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Dev9IWi.jpg [ 8.85 KiB | Viewed 411 times ]

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Joined: 04 Jan 2015
Posts: 2292
Re: ABCD and EFGH are rectangles. What is the area of the shaded region?  [#permalink]

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26 Jun 2018, 21:20

Solution

Given:
• ABCD and EFGH are rectangles
• Side lengths of ABCD = 3x and 2x
• Side lengths of EFGH = x and y

To find:
• The area of the shaded region

Approach and Working:
We can write the area of the shaded region as
• Area of rectangle ABCD – area of rectangle EFGH
= $$3x * 2x – x * y$$
= $$6x^2 – xy$$

Hence, the correct answer is option D.

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ABCD and EFGH are rectangles. What is the area of the shaded region?  [#permalink]

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26 Jun 2018, 21:49
Outer rectangle area: length * breadth = 3x * 2x = $$6x^{2}$$
Inner rectangle area: xy

Shaded = Outer - inner = $$6x^{2}$$ - xy
ABCD and EFGH are rectangles. What is the area of the shaded region? &nbs [#permalink] 26 Jun 2018, 21:49
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