find the area of a shape formed by joining a rectangle and two semicircles.

Question

a shape is formed by joining a rectangle and two semicircles. the rectangle is 90 m long and 56 m wide. find the area of the shape. use the value 3.14 for pi, and do not round your answer.

Answer 1

Assuming, both semicircles are on short ends and the diameter is 56m (same as short end length), then you would find the area of the rectangle (56m*90m) plus the area of a circle with radius 28m (3.14(28)^2).

Likewise for the semicircles being on long ends, but instead of using 28m for r in pi*r^2, we'd use 45m.

Then for one on a short and one on a long it would be the area of the rectangle plus half the area of the smaller circle plus half the area of the larger circle.

If the semicircles are anything other than matching the length of the sides, then you'd have the following generalization.

rectB1 = base 1 of 56m

rectB2 = base 2 of 90m

scDia1 = semicircle diameter 1

scDia2 = semicircle diameter 2

pi = 3.14

rectB1*rectB2+((pi*(scDia1 / 2)^2) / 2) +((pi*(scDia2 / 2)^2) / 2)