Find the perimeter and area of the given composite shape.

Question

https://ibb.co/TDLfk49D

Answer 1

Answer 2

Hi CIhhf! The composite shape you showed is a Trapezoid with a shark bite taken out of it in the shape of a half-circle. Let's find the area of both shapes, and subtract them.

1. Find the area of the Trapezoid:

Area of a trapezoid formula is A = 1/2 * (b₁+b₂) * h

where b1 is the first base (the length of the bottom of the trapezoid) = 90 cm

b₂ is the second base (the length of the top of the trapezoid) = 60 cm

h is the height (which in this case, is twice the radius of the half-circle) = 30 cm

Plugging in those three values: A= 1/2 * (90 + 60) * 30 = 2250 cm²

1. Find the area of the Half-Circle:
2. The area of a circle formula is A=πr², where r is the radius. Since the radius in the picture is given as 15 cm, plug 15 in for r. A = π(15²) = 706.86 cm²
3. Divide that answer by two, because we have half of the circle! = 353.43 cm²

1. Subtract the area of the half-circle from the area of the Trapezoid, since that area is "missing":

2250 cm² - 353.43 cm² = 1896.57 cm²

Hope that helped!