Question

Help me!! Luv ya :)
The figure below shows Mikail’s semi-circular patio. The shaded region represents the tiled portion of the patio.

Two concentric semi-circles, with the area between them shaded. The diameter of the larger one is 14 feet.

The width of the tiled portion is 1.5 feet. What is the area of the tiled portion of the patio, rounded to the nearest whole square foot?

59 square feet

29 square feet

44 square feet

70 square feet

Answer 1

You need to do the bigger half circle minus the small half circle to leave you with the tiled region.

Area of Circle = pi * r^2
Therefore, Area of 1/2 Circle = 1/2 * pi * r^2

Radius of big circle = 14/2 = 7
Radius of small circle = 14-1.5-1.5 / 2 = 11/2 = 5.5

Big - Small = (1/2 * pi * 7^2) - (1/2 * pi * 5.5^2) = 29 square feet

Answer 2

Thank you!! That helped a lot.