Question

What is the area of this polygon? 28.5 units² 34.5 units² 37.5 units² 40.5 units² 6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)

Answer 1

Option B.

Explanation:

The given vertices of the polygon are (-6,-2),(-5,1),(-1,4),(1,1),(5,3),(1,-2).

We need to find the area of the polygon.

Plot the given vertices and on a coordinate plane and draw the polygon. Divide the polygon in 4 parts as shown below.

Area of rectangle is

`A=length* width`

Area of triangle is

`A=(1)/(2)* base* height`

Area of each figure is

`A_1=(1)/(2)* 1* 3=1.5`

`A_2=(1)/(2)* 6* 3=9`

`A_3=(1)/(2)* 4* 3=6`

`A_4=6* 3=18`

Area of polygon is

`A=A_1+A_2+A_3+A_4`

`A=1.5+9+6+18=34.5`

The area of polygon is 34.5 units².

Therefore, the correct option is B.