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
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sanju09
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The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
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Lucknow-226001
www.manyagroup.com
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ballubalraj
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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.
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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sanju09
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both explanations are same & goodkstv wrote:@ ballubalraj
Please let me know if the above explantion is not good.
What if it is v good.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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gmatguytoday
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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!
