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.)

Question

asked Sep 21, 2023 172k views

1 Answer

David Jarrin · Answer 1 · 2023-09-25T01:05:05+0000

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