The problem is to find the area of the given polygon. The polygon consists of a rectangle and two triangles. The formula for the area of a rectangle is given as $bh$, and the formula for the area of a triangle is given as $\frac{1}{2}bh$.

1. Problem Description

The problem is to find the area of the given polygon. The polygon consists of a rectangle and two triangles. The formula for the area of a rectangle is given as $bh$, and the formula for the area of a triangle is given as $\frac{1}{2}bh$.

2. Solution Steps

First, we observe that the polygon is composed of a rectangle and two triangles on either side of the rectangle. The rectangle has a base of 12 ft and a height of 10 ft (5 ft + 5 ft). The two triangles are identical. The base of each triangle is 5 ft, and the height is the difference between the total length (12 ft) and the length of the base of the rectangle, divided by

2. Since the rectangle base is 12 ft, the height of each triangle is 5 ft.

Area of the rectangle:

$Area_{rectangle} = base \times height = 12 ft \times 10 ft = 120 ft^2$

Area of one triangle:

$Area_{triangle} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 5 ft \times 5 ft = \frac{25}{2} ft^2 = 12.5 ft^2$

Since there are two triangles, the total area of the two triangles is:

$Area_{2 triangles} = 2 \times Area_{triangle} = 2 \times 12.5 ft^2 = 25 ft^2$

The total area of the polygon is the sum of the area of the rectangle and the area of the two triangles:

$Area_{total} = Area_{rectangle} + Area_{2 triangles} = 120 ft^2 + 25 ft^2 = 145 ft^2$

3. Final Answer

The area of the polygon is 145 $ft^2$.