The area of a trapezoid is 18sq. ft and the sum of its bases is 6 ft. Find the area of a square whose side is equal to the height of the trapezoid.
A=[(a+b)/2]h
18 = 3h
6 = h
A of a square = s^2
A = 6 * 6
The area of the trapezoid is 18square millimeters.
What is the trapezoid's height, h?
h=
millimeters
To find the area of the square, we first need to find the height of the trapezoid.
The formula for the area of a trapezoid is given by:
Area = (1/2) * (base1 + base2) * height
We are given that the area of the trapezoid is 18 sq. ft and the sum of its bases is 6 ft. We can set up the equation as follows:
18 = (1/2) * (base1 + base2) * height
6 = base1 + base2 (Since the sum of the bases is 6 ft.)
From the second equation, we can express base1 in terms of base2:
base1 = 6 - base2
Substituting this into the first equation, we get:
18 = (1/2) * (base2 + (6 - base2)) * height
18 = (1/2) * (6) * height
18 = 3 * height
height = 6 ft / 3
height = 2 ft
Now that we have the height of the trapezoid, we can calculate the area of the square. Since the side length of the square is equal to the height of the trapezoid, the area of the square is given by:
Area of square = side length^2
Substituting the value of the height, we get:
Area of square = 2 ft * 2 ft
Area of square = 4 sq. ft
Therefore, the area of the square is 4 sq. ft.