Question

the polygon shown is decomposed into two triangles. how can you find the area of the shaded polygon? i can add the area of the two triangles. what is the area of the top triangle? area of the top triangle = 9 square units. what is the area of the bottom triangle? area of the bottom triangle = 6 square units. area = \frac{1}{2}\cdot base\cdot height = \frac{1}{2}\cdot6\cdot5

Explanation:

Step1: Calculate the area of the top triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).
For the top triangle, assume the base \(b = 6\) units and height \(h= 3\) units.
\(A_{top}=\frac{1}{2}\times6\times3\)
\(A_{top}=9\) square units.

Step2: Calculate the area of the bottom triangle

For the bottom triangle, assume the base \(b = 6\) units and height \(h = 2\) units.
\(A_{bottom}=\frac{1}{2}\times6\times2\)
\(A_{bottom}=6\) square units.

Step3: Calculate the area of the shaded polygon

Since the shaded polygon is composed of two triangles, we add the areas of the two triangles.
\(A = A_{top}+A_{bottom}\)
\(A=9 + 6\)

Answer:

The area of the shaded polygon is \(15\) square units.