Question

Find the area of the shaded portion in the equilateral triangle with sides 6 assuming the central point of each arc is its corresponding vertex.

Answer 1

do you have a photo

Answer 2

Angle of arc = 60 deg

Area of shaded region = area of triangle - 3(area of arc)

r = 3

b = 6

h^2 + 3^2 = 6^2

h^2 = 36 - 9

h^2 = 27

h = 3√3

Area of triangle:
A = (1/2)(6)(3√3) = 3(3√3) = 9√3

Area of arc:
r = 3
angle = 60 deg

Area of arc = (1/6)(area of circle)

Area of circle:
A = pi (3^2) = 9pi

Area of arc = (1/6)(9pi) = 3pi/2

There are 3 such arcs:
Area of arcs = 3(3pi/2) = 9pi/2

Area of shaded region:
9√3 - 9pi/2 = 1.45

Answer 3

thank you so much!

Answer 4

u r welcome :)