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3 years ago

Find the area of a 8-gon with radius length 6. Round to a whole number.

Mathematics

1 answer:

djyliett [7]3 years ago

7 0

Answer:

Area = 102

Step-by-step explanation:

Length 1 side of the octagon.

The formula for the side of an octagon (given the radius of 6) is

s^2 = 2*R^2(1 - cos(45) )

s^2 = 2*6^2(1 - sqrt(2)/2)

s^2 = 72 ( 1 - 0.707)

s^2 = 72*0.2929

s^2 = 21.09

s = sqrt(21.09)

s = 4.5922

===============

Height of one triangle =

H = R * cos(22.5)

H = 6 * 0.9329

H = 5.5433

===============

Area of 1 triangle

Area = 1/2 * s * h

Area = 1/2 * 4.5922*5.4433

Area = 12.7279

Area of 8 triangles

Area of 8 triangles = 1 triangle * 8

Area of 8 triangles = 101.82

Rounded that comes to 102

Comment

I'm sure you can find a formula for this on the internet, but it this is the way the formula works and if you break it down step by step, you can see how the formula works.

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