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What is the area of this polygon?

A. 42.5 units²
b. 41.5 units²
c. 35.5 units²
d. 29.5 units²

What is the area of this polygon? A. 42.5 units² b. 41.5 units² c. 35.5 units² d. 29.5 units-example-1

1 Answer

2 votes

Answer:

c

Explanation:

divide the diagram in three parts

i. quadrilateral with vertices (1,1),(1,-2),(6,-2),(6,4),two vertical sides are parallel.

2.triangle with vertices (-6,1),(1,1),(-1,3)

3. triangle with vertices (-6,1),(1,1),(1,-2)

area=\frac{(4+2)+(1+2)}{2}×(5-1)+[\frac{1}{2}×(6+1)×2+\frac{1}{2}×(6+1)×(1+2)]

=\frac{9}{2}×4+[\frac{1}{2}×7×2+\frac{1}{2}×7×3

=\frac{36}{2}+\frac{14}{2}+\frac{21}{2}

=\frac{36+14+21}{2}

=\frac{71}{2}

=35 \frac{1}{2}

or =35.5 units²

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