A right triangle is removed from a rectangle. We need to find the area of the shaded region. The rectangle has dimensions 8 ft and 7 ft. The right triangle has legs of lengths 4 ft and 2 ft (7 ft - 5 ft = 2 ft).

1. Problem Description

A right triangle is removed from a rectangle. We need to find the area of the shaded region. The rectangle has dimensions 8 ft and 7 ft. The right triangle has legs of lengths 4 ft and 2 ft (7 ft - 5 ft = 2 ft).

2. Solution Steps

First, calculate the area of the rectangle.

$Area_{rectangle} = length \times width$

$Area_{rectangle} = 8 ft \times 7 ft = 56 ft^2$

Next, calculate the area of the right triangle.

$Area_{triangle} = \frac{1}{2} \times base \times height$

$Area_{triangle} = \frac{1}{2} \times 4 ft \times 2 ft = 4 ft^2$

Now, subtract the area of the triangle from the area of the rectangle to find the area of the shaded region.

$Area_{shaded} = Area_{rectangle} - Area_{triangle}$

$Area_{shaded} = 56 ft^2 - 4 ft^2 = 52 ft^2$

3. Final Answer

52 $ft^2$