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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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  35% (medium)

Question Stats:

70% (02:11) correct 30% (01:04) wrong based on 26 sessions

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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
2018-03-08_1321.png [ 13.59 KiB | Viewed 322 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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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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.
Attachments

trapezoid.png
trapezoid.png [ 9 KiB | Viewed 251 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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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
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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A dam has the dimensions indicated in the figure. Find the area of thi

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