Answer:
33 square units
Step-by-step 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.
The area of a rectangle is simply [tex]A = bh[/tex], 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:
[tex]A = (6)(4)\\A = 24[/tex]
The area of the rectangle is 24 square units
The area of a triangle is simply [tex]A = \frac{1}{2} bh[/tex].
The base of each triangle is 3, and the height of each triangle is also 3.
Substituting in the values, we get:
[tex]A = \frac{1}{2} (3)(3)\\A = \frac{1}{2} (9)\\A = 9 / 2\\A = 4.5[/tex]
The area of each triangle is 4.5 square units
To get the area of the polygon, we simply add up the area of the rectangle and both triangles
[tex]A = 24 + 4.5 + 4.5\\A = 24 + 9\\A = 33[/tex]
The total area of the polygon is 33 square units.
