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by sanju09 » Wed May 19, 2010 3:22 am
The lengths in the rectangle attached below are in inches. What is the shaded area in square inches?
(A) 70
(B) 38
(C) 34
(D) 21
(E) 8


[spoiler]source: www.analyzemath.com[/spoiler]
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by kstv » Wed May 19, 2010 3:30 am
IMO B
Area of Rect = 7*10
Area of the triangles = 1/2(42+16+6) = 32
Shaded area = 70-32
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by ballubalraj » Wed May 19, 2010 3:37 am
Please see the attached diagram:

lenght x = 7 - 4 = 3

Now, lets calculate the areas of trianges denoted by A, B, C

Area of A = (7*6)/2 = 21
Area of B = (4*4)/2 = 8
Area of C = (3*2)/2 = 3

Area of rectangle = 10*7 = 70

Area of shaded portion = Total area of rectangle - Total area of un-shaded portion = 70 - (21+8+3) = 38

Answer B.

There is another approach (but much time consuming for this example) to solve this problem. Calculate the sides of the trapezium by applying pythagoras theorem and then calculate the area of the trapezium by formula = (sum of parallel sides)*Height/2.

Please let me know if the above explantion is not good.
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by kstv » Wed May 19, 2010 3:47 am
@ ballubalraj
Please let me know if the above explantion is not good.
What if it is v good.
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by sanju09 » Wed May 19, 2010 3:50 am
kstv wrote:@ ballubalraj
Please let me know if the above explantion is not good.
What if it is v good.
both explanations are same & good
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by gmatguytoday » Thu May 20, 2010 4:47 pm
ballubalraj wrote:Please see the attached diagram:

lenght x = 7 - 4 = 3

Now, lets calculate the areas of trianges denoted by A, B, C

Area of A = (7*6)/2 = 21
Area of B = (4*4)/2 = 8
Area of C = (3*2)/2 = 3

Area of rectangle = 10*7 = 70

Area of shaded portion = Total area of rectangle - Total area of un-shaded portion = 70 - (21+8+3) = 38

Answer B.

There is another approach (but much time consuming for this example) to solve this problem. Calculate the sides of the trapezium by applying pythagoras theorem and then calculate the area of the trapezium by formula = (sum of parallel sides)*Height/2.

Please let me know if the above explantion is not good.

Why do I not get the same answer by using pythagorean theorem....I get an irrational number....I think too many hours of studying has finally gotten to me!
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