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# A dam has the dimensions indicated in the figure. Find the area of thi

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
A dam has the dimensions indicated in the figure. Find the area of thi  [#permalink]

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08 Mar 2018, 02:23
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Difficulty:

25% (medium)

Question Stats:

83% (02:38) correct 17% (02:10) wrong based on 27 sessions

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A dam has the dimensions indicated in the figure. Find the area of this isosceles trapezoid.

(A) 1300

(B) 1560

(C) 1400

(D) 1440

(E) It cannot be determined from the information given.

Attachment:

2018-03-08_1321.png [ 13.59 KiB | Viewed 693 times ]

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: A dam has the dimensions indicated in the figure. Find the area of thi  [#permalink]

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08 Mar 2018, 02:24
Bunuel wrote:
A dam has the dimensions indicated in the figure. Find the area of this isosceles trapezoid.

(A) 1300

(B) 1560

(C) 1400

(D) 1440

(E) It cannot be determined from the information given.

Attachment:
2018-03-08_1321.png

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Re: A dam has the dimensions indicated in the figure. Find the area of thi  [#permalink]

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08 Mar 2018, 02:56
Bunuel wrote:
A dam has the dimensions indicated in the figure. Find the area of this isosceles trapezoid.

(A) 1300

(B) 1560

(C) 1400

(D) 1440

(E) It cannot be determined from the information given.

Attachment:
The attachment 2018-03-08_1321.png is no longer available

When calculating areas, it is very useful to divide a complex shape into simpler ones.
This is an Alternative approach.

Since our trapezoid is isosceles, the two triangles on the sides are identical and have equal bases.
So, each has a base of (70 - 50)/2 = 10
Using the Pythagorean triplet 5-12-13, we know that the height of each triangle is 24.
So, our total area is (square + 2 triangles) = 50*24 + 10*24/2 + 10*24/2 = 60*24 = 1440

Attachments

trapezoid.png [ 9 KiB | Viewed 594 times ]

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Re: A dam has the dimensions indicated in the figure. Find the area of thi  [#permalink]

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08 Mar 2018, 03:31
After disecting the figure we can simply put Area of Trapeziod = {Height * (upper + lower side length)}/2
i.e {24*(50+70)}/2 = 1440

Hence C
Re: A dam has the dimensions indicated in the figure. Find the area of thi   [#permalink] 08 Mar 2018, 03:31
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