A new park is being built in the shape of a trapezoid, as show in the diagram below.
A trapeziod has a base width of 20, a top width of 10, and one side of it is a striaght line thats height is 12.5, and the other side is a slant with a height of 6.4
The builders will cover the ground with a solid rubber surface to ensure the children playing have a safe and soft place to land when they jump or fall.
How many square yards of rubber will be needed for this park?
To calculate the total area of the trapezoid park, we need to find the area of the two trapezoids formed by the slant side.
First, calculate the area of the trapezoid with bases width of 20 and 10, and height of 12.5:
Area = (1/2) * (base1 + base2) * height
Area = (1/2) * (20 + 10) * 12.5
Area = (1/2) * 30 * 12.5
Area = 375 square yards
Next, calculate the area of the triangle formed by the slant side with height 6.4:
Area = (1/2) * base * height
Area = (1/2) * 10 * 6.4
Area = 32 square yards
Add the two areas together to find the total area of the park:
Total area = 375 + 32
Total area = 407 square yards
Therefore, 407 square yards of rubber will be needed for this park.