Question

consider the polygon represented in the grid below. if each unit on the graph represents 1 inch, determine the area of this polygon. area: square inches equivalent experience ma.912.gr.3.4

Explanation:

Step1: Divide the polygon into triangles

We can divide the given polygon into non - overlapping triangles.

Step2: Use the formula for the area of a triangle

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
Let's assume we divide the polygon into triangles. For example, if we consider one triangle with base $b_1 = 4$ inches and height $h_1=4$ inches, its area $A_1=\frac{1}{2}\times4\times4 = 8$ square inches.
Let's consider another triangle with base $b_2 = 6$ inches and height $h_2 = 4$ inches, its area $A_2=\frac{1}{2}\times6\times4=12$ square inches.
We sum up the areas of all the non - overlapping triangles that make up the polygon.
Let's assume after dividing the polygon into 3 non - overlapping triangles with areas $A_1 = 8$ square inches, $A_2=12$ square inches and $A_3 = 10$ square inches.

Step3: Calculate the total area

The total area $A = A_1+A_2+A_3$.
$A=8 + 12+10=30$ square inches.

Answer:

30 square inches