Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
882 square inches
882 square inches
864 square inches
864 square inches
756 square inches
756 square inches
648 square
inches
756 square inches
To find the area of a trapezoid-shaped tabletop, we can create a rectangle around the trapezoid by extending the shorter base to form a right angle with the longer base.
Let's say the longer base of the trapezoid is 18 inches and the shorter base is 12 inches. The height of the trapezoid is 14 inches.
We can then find the area of the rectangle, which would have a length of 18 inches and a width of 14 inches.
Area of rectangle = length x width
Area of rectangle = 18 inches x 14 inches
Area of rectangle = 252 square inches
Since the trapezoid only covers a portion of the rectangle, we need to find the area of the trapezoid as a fraction of the rectangle's area.
Area of trapezoid = (shorter base + longer base) x height / 2
Area of trapezoid = (12 inches + 18 inches) x 14 inches / 2
Area of trapezoid = 30 inches x 14 inches / 2
Area of trapezoid = 420 square inches
Therefore, the area of the trapezoid-shaped tabletop is 420 square inches.