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dexar [7]
3 years ago
7

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

Mathematics
1 answer:
koban [17]3 years ago
3 0

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.

<h3>Area of the rectangle</h3>

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

<h3>Area of the triangles</h3>

The area of a triangle is simply A = \frac{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 = \frac{1}{2} (3)(3)\\A =  \frac{1}{2} (9)\\A =  9 / 2\\A = 4.5

The area of each triangle is 4.5 square units

<h3>Area of the polygon</h3>

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.

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