Question

Use area to solve the problems practice.
A designer wants to estimate the area of a trapezoid-shaped stage. Each square represents one square foot. The designer decides to find the area by composing a rectangle. What is the length of the base of the rectangle in feet?
(1 point)

Answer 1

To find the length of the base of the rectangle, we need to create a rectangle that is similar in shape to the trapezoid stage.

First, we can divide the trapezoid into two shapes - a rectangle and a triangle. Then, we can rearrange the triangle to make it fit into the rectangle.

Let the height of the trapezoid be 7 feet, the base of the trapezoid be 8 feet, and the top side of the trapezoid be 5 feet.

The area of the trapezoid is:
Area = (1/2) * (base1 + base2) * height
Area = (1/2) * (8 + 5) * 7
Area = (1/2) * 13 * 7
Area = 91 square feet

Now, let's arrange the triangle into the rectangle:
The height of the rectangle is 7 feet.
The width of the rectangle is the base of the trapezoid (8 feet).
Therefore, the length of the base of the rectangle is also 8 feet.

The length of the base of the rectangle is 8 feet.