ind the area of the regular 24​-gon with radius 13 mm.

Question

need help

Answer 1

the circle circumscribes the polygon; the polygon is inside the circle

the radii form 24 congruent triangles

find the area of one triangle and multiply the answer by 24

the formula for one of the triangles given the radius is:

A=(1/2)(r²)(sin[360/n])

A=(1/2)(13²)sin([360/24])  (360/24 gives the 24 equal angles at the center of the circumscribed  circle inside each triangle)

A=(1/2)(169)sin(15º)

A=(1/2)(169)(0.258819)  

A=(1/2)(43.7404)

A=21.8702 square millimeters for one of the 24 congruent triangles

multiply this answer by 24 to get the area of the entire 24-gon

A=24*21.8702

A=524.885 square millimeters is the area of the 24-gon