Question

Triangle fgh is inscribed in circle o the length of radius oh is 6 and fh is congruent to og. what is the area of the sector formed by angle foh

Answer 1

Given :
Triangle fgh is inscribed in circle o

oh = 6 = radius of the circle 
∵ fh is congruent to og

∴ fh = og = radius og the circle = 6

∵ of = radius of the circle = 6

∴ oh = fh = of = radius of the circle = 6

∴ Δ foh is Equilateral Triangle

∴∠ foh = 60° ⇒⇒⇒ property of the equilateral Triangle

∵ total area of the circle = π r²  and total central angle of the circle = 360°
∴ Area of sector foh = (60°/360°) * π r²
∴ Area of sector foh = (60°/360°) * π * 6² ≈ 18.85

The answer is:

the area of the sector formed by angle foh  = 18.85