Question

a regular octagon (a polygon with 8 equal sid3s) is inscribed in a circle of radius 19.9cm. find the perimeter of the octagon

Answer 1

Perimeter of an octagon

radius R = 19.9 cm

then To find perimeter

Multiply 8 times lenghts of octagon

with height=

internal angle is= 360/8 = 45°

Now apply rule of Sines

then sin 45/ lside = sin ( 180-45)/2/ radius

Therefore

Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm

Now multiply 8 times this lenght side to find perimeter

8x 15.23 = 121.84 cm