Question

The atrium was built in the shape shown. Find the area and perimeter of the atrium. Round to the nearest whole unit. (Dimensions are in m.)

Answer 1

Total area

A = semi circle + triangle.

1. Area of the semi circle:

`A\text{ = }(\pi* r^2)/(2)=\text{ }(\pi*3^2)/(2)=\text{ 14.14 }`

2. Area of the triangle:

`A\text{ = }(b* h)/(2)`

h = 6; to find base we use the Pythagoras theorem, as follows:

`b=\sqrt[]{10^2-6^2}=\text{ 8}`

Then,

`A\text{ = }\frac{8\text{ x 6}}{2}\text{ = 24}`

Total area = 14 + 24 = 38 m²

Perimeter =

6 (π + 2) + 10 + 8 = 49 m