Question

Express answer in exact form.

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.

Answer 1

A chord and a radius form an equilateral triangle.
The area of the larger segment is:
A = 5/6 r² π + r²√3/2 = 5/6 · 64 · 3.14 + 32 · 1.73 =
= 167.47 + 55.36 = 222.83 in²