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

Answer:

Option B.

Step-by-step 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

$A=length\times width$

Area of triangle is

$A=\dfrac{1}{2}\times base\times height$

Area of each figure is

$A_1=\dfrac{1}{2}\times 1\times 3=1.5$

$A_2=\dfrac{1}{2}\times 6\times 3=9$

$A_3=\dfrac{1}{2}\times 4\times 3=6$

$A_4=6\times 3=18$

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.