Answer:
1300 - 200π as an exact answer, or
671.68 units² if you use a calculator
Step-by-step explanation:
We have a trapezoid with half of a circle cut out of it. First we will calculate the area of the full trapezoid, then subtract the area of the semi circle...
The area of a trapezoid is
A = (1/2)(B + b)h
Area is one-half of the sum of the bases times the height
The bases are 80 and 50, it doesn't matter which one you call B or b. The height is the radius of the semi circle, which is 20, so we have
A = (1/2)(80 + 50)(20)
A = (1/2)(130)(20)
A = (1/2)(2600)
A = 1300 cm²
The area for a semi circle is
A = (πr²)/2 so we have
A = (π(20²))/2
A = (400π)/2
A = 200π
So the are of the figure is
1300 - 200π units² as an exact answer, or
671.68 units² if you use a calculator
