Question

3 what is the area of the polygon? show your work. solution

Explanation:

Step1: Divide the polygon

Divide the polygon into two triangles by drawing a diagonal.

Step2: Find base and height of one triangle

Assume the grid - squares have a side - length of 1 unit. For one of the triangles, count the base and height. Let's say the base \(b = 4\) units and the height \(h = 2\) units.

Step3: Calculate area of one triangle

Use the formula for the area of a triangle \(A_{\triangle}=\frac{1}{2}bh\). Substituting \(b = 4\) and \(h = 2\), we get \(A_{\triangle}=\frac{1}{2}\times4\times2=4\) square units.

Step4: Calculate area of the polygon

Since the polygon is composed of two congruent triangles, the area of the polygon \(A = 2\times A_{\triangle}\). So \(A=2\times4 = 8\) square units.

Answer:

8 square units