A geometry problem by edil tizon

Geometry Level 2

What is the area, in square meters, of the shaded part of the rectangle?

A. 40

B. 48

C. 56

D. 74

48 56 74 40

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2 solutions

Omkar Kulkarni
Jan 21, 2015

The area of the shaded region is the area of the rectangle minus the sum of the areas of the two triangles.

= l b 1 2 b 1 h 1 2 b 2 h = lb - \frac {1}{2} b_{1} h - \frac {1}{2} b_{2} h

= ( 6 ) ( 16 ) 1 2 h ( b 1 + b 2 ) = (6)(16) - \frac {1}{2} h ( b_{1} + b_{2} )

= ( 6 ) ( 16 ) 1 2 ( 6 ) ( 16 ) = (6)(16) - \frac {1}{2}(6)(16)

= 1 2 ( 6 ) ( 16 ) = 48 = \frac {1}{2} (6)(16) = \boxed {48}

area of shaded region = area of unshaded region = one half of the area of the rectangle = 0.5 * 16 * 6 = 48 square meters

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