The area of a trapezoid is 18 square feet, and the sum of its base is 6 feet. Find the area of a square whose sides are equal to the height of the trapezoid.
To find the area of the trapezoid, we can use the formula:
Area = (1/2) * (base1 + base2) * height
Since the sum of the bases is 6 feet, let's denote the bases as x and 6-x. The height of the trapezoid will be equal to the side of the square, so the area of the trapezoid will be:
18 = (1/2) * (x + 6-x) * side
18 = (1/2) * 6 * side
18 = 3 * side
side = 18 / 3
side = 6 feet
So, the side of the square is 6 feet. The area of a square is given by the formula:
Area = side^2
Area = 6^2
Area = 36 square feet
Therefore, the area of the square with sides equal to the height of the trapezoid is 36 square feet.