High School

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 units²

Answer :

Answer:

c

Step-by-step 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