Question

What is the area of the polygon? Show your work.​

Answer 1

33 square units

Explanation:

Assuming that each line on this grid increases by a value of one, the area of the polygon can be determined by breaking it down into a large rectangle and two smaller triangles.

Area of the rectangle

The area of a rectangle is simply
`A = bh`, where b represents the base and h represents the height.

Counting the size of each side, we can determine that they are 6 units for the base and 4 units for the height.

Substituting in the values, we get:

`A = (6)(4)\\A = 24`

The area of the rectangle is 24 square units

Area of the triangles

The area of a triangle is simply
`A = (1)/(2) bh`.

The base of each triangle is 3, and the height of each triangle is also 3.

Substituting in the values, we get:

`A = (1)/(2) (3)(3)\\A = (1)/(2) (9)\\A = 9 / 2\\A = 4.5`

The area of each triangle is 4.5 square units

Area of the polygon

To get the area of the polygon, we simply add up the area of the rectangle and both triangles

`A = 24 + 4.5 + 4.5\\A = 24 + 9\\A = 33`

The total area of the polygon is 33 square units.