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# If the area of the trapezoid GECD above is 90, what is the area of ∆ E

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Math Expert
Joined: 02 Sep 2009
Posts: 49251
If the area of the trapezoid GECD above is 90, what is the area of ∆ E  [#permalink]

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05 Oct 2017, 01:40
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Difficulty:

35% (medium)

Question Stats:

81% (01:43) correct 19% (02:13) wrong based on 32 sessions

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If the area of the trapezoid GECD above is 90, what is the area of ∆ EFG?

(A 60
(B) 64
(C) 66
(D) 68
(E) 72

Attachment:

2017-10-04_1125_002.png [ 7.48 KiB | Viewed 583 times ]

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Re: If the area of the trapezoid GECD above is 90, what is the area of ∆ E  [#permalink]

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05 Oct 2017, 02:39
If the area of the trapezoid GECD above is 90, what is the area of ∆ EFG?

* Here we have to consider ABCD be a rectangle.

By Figure we know DC =12, GD = 2

Area of trapezoid GECD = 1/2 * DC* (GD+EC) = 1/2 *12*(2+EC) = 90 given
=> EC = 13
=> EC = FD = 13 =FG+GD = FG+2 => FG = 11

Area of ∆ EFG = 1/2*FG*EF = 1/2*11*12 = 66

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Re: If the area of the trapezoid GECD above is 90, what is the area of ∆ E  [#permalink]

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09 Oct 2017, 16:51
Bunuel wrote:

If the area of the trapezoid GECD above is 90, what is the area of ∆ EFG?

(A 60
(B) 64
(C) 66
(D) 68
(E) 72

Attachment:
2017-10-04_1125_002.png

We see that the height of the trapezoid is 12, and base 1 = 2. If we let base 2 = n, we can determine n with the following formula:

area = (base 1 + base 2)/2 x height

90 = (2 + n)/2 x 12

180 = 24 + 12n

156 = 12n

13 = n

Thus, the base of triangle EFG is 13 - 2 = 11. We now can determine the area:

area = ½ x base x height

area = ½ x 11 x 12 = 66

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Re: If the area of the trapezoid GECD above is 90, what is the area of ∆ E &nbs [#permalink] 09 Oct 2017, 16:51
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