What is the area of the shaded region in the figure above ?

Question

https://gmatclub.com/forum/download/file.php?id=28395 What is the area of the shaded region in the figure above ? (A) 72 (B) 57 (C) 55 (D) 54 1/2 (E) 49 1/2 Untitled.png

BrentGMATPrepNow · Answer

Area of shaded region = (area of large 8 x 9 rectangle) - (area of unshaded trapezoid)
= (72) - (4 + 6)(3)/2
= 71 - 15
= 57

Answer: B

Abhishek009 · Answer

I am dividing the figure into 4 parts.

A - A rectangle with length 6 and breadth 4
B - A rectangle with length 6 and breadth 4

C - A rectangle with length 3 and breadth 2

D - A triangle with Base 2 and Height 3

Area of the entire figure = Area of A + Area of B + Area of C + Area of D

Area of A = 24
Area of B = 24
Area of C = 6
Area of D = 3

Total Area of the entire figure = 57 (24 + 24 + 6 + 3)

Hence answer is (B) 57

NandishSS · Answer

Area of the shaded region in the figure= Area of the region(Rectangle) - Area of unshaded region(trapezium)

Area of rectangle = 8*9 =72

Area of trapezium = (a+b/2)*h = (10/2)*3 = 15

72-15= 57

Hence B

*Corrected Typo*

KarishmaB · Answer

Note that the slanting line has end points at (4, 6) and (6, 9). 
Area of the trapezium so formed = (1/2)*3*(4 + 2) = 9

Area of the rest of the shaded rectangle = 6*8 = 48

Total shaded area = 9 + 48 = 57

Answer (B)

Wildflower · Answer

Here's another way to do this problem:

Area of shaded region = Area of square - area of unshaded region (trapezoid, in this case)

Area of square = B*H --> 8*9 = 72

Area of unshaded region = (B1+B2)/2 *H --> (6+4)/2 * 3 =15

Area of shaded region = 72-15 = 57

HarshavardhanR · Answer

Observe that -> Area of the shaded region = Area of the big rectangle (created by the x axis, the y axis, x = 9, and y = 8) - Area of the unshaded trapezium 
 Area of the big rectangle = 9 x 8 = 72 
 Area of the trapezium =  \frac{1}{2}  x (sum of parallel sides) x (distance between parallel sides) =  \frac{1}{2}  x (6+4) x (3) = 15 
 So, area of the shaded region = 72 - 15 =  57. Choice B .

---
Harsha

What is the area of the shaded region in the figure above ?

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What is the area of the shaded region in the figure above ?

Prep Toolkit

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