Find the area of the green polygon

Geometry Level pending

Find the area of the green polygon.


The answer is 211.5.

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2 solutions

Masbahul Islam
Oct 31, 2017

The area bounded by the points

(0,0)

(18,3)

(24,12)

(12,15) and

(3,9)

=0.5x{18x12-24x3+24x15-12x12+12x9-15x3}

=211.5

A 1 = trapezoid = 1 2 ( 3 + 12 ) ( 6 ) = 45 A_1=\text{trapezoid}=\dfrac{1}{2}(3+12)(6)=45

A 2 = triangle = 1 2 ( 3 ) ( 9 ) = 13.5 A_2=\text{triangle}=\dfrac{1}{2}(3)(9)=13.5

A 3 = triangle = 1 2 ( 3 ) ( 12 ) = 18 A_3=\text{triangle}=\dfrac{1}{2}(3)(12)=18

A 4 = trapezoid = 1 2 ( 3 + 12 ) ( 6 ) = 45 A_4=\text{trapezoid}=\dfrac{1}{2}(3+12)(6)=45

A 5 = triangle = 1 2 ( 3 ) ( 18 ) = 27 A_5=\text{triangle}=\dfrac{1}{2}(3)(18)=27

A g r e e n = 15 ( 24 ) 45 13.5 18 45 27 = A_{green}=15(24)-45-13.5-18-45-27= 211.5 \boxed{211.5}

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