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

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

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New post 08 Mar 2018, 02:23
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

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

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

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

(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

(D) is our answer.
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Re: A dam has the dimensions indicated in the figure. Find the area of thi  [#permalink]

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New post 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
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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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