Tuesday
June 18, 2013

# Homework Help: Area Geometry

Posted by hope on Tuesday, April 10, 2012 at 12:07am.

Find the area of a decagon with a radius of 4mm.

Find the area of an octagon with a radius of 10 cm.

• Area Geometry - Bosnian, Tuesday, April 10, 2012 at 2:25am

Area of a regular polygon:

A = ( 1 / 2 ) * n * r ^ 2 * sin ( 360 ° / n )

The area of a decagon:

( n = 10 )

( r = 4 mm )

( sin 36 ° = sqrt [ 10 - 2 sqrt ( 5 ) ] / 4

A = ( 1 / 2 ) * 10 * 4 ^ 2 * sin ( 360 ° / 10 )

A = 10 / 2 * 16 * sin ( 36 ° )

A = 5 * 16 * sin ( 36 ° )

A = 5 * 16 * sqrt [ 10 - 2 sqrt ( 5 ) ] / 4

A = 5 * 16 / 4 * sqrt [ 10 - 2 sqrt ( 5 ) ]

A = 5 * 4 * sqrt [ 10 - 2 sqrt ( 5 ) ]

A = 20 * 2.351141

A = 47.02282 mm ^ 2

The area of a octagon:

( n = 8 )

( r = 10 mm )

( sin 45 ° = 1 / sqrt ( 2 ) = sqrt ( 2 ) / 2 )

A = ( 1 / 2 ) * 8 * 10 ^ 2 * sin ( 360 ° / 8 )

A = 8/ 2 * 100 * sin ( 45 ° )

A = 4 * 100 * sin ( 45 ° )

A = 400 * sqrt ( 2 ) / 2

A = ( 400 / 2 ) * sqrt ( 2 )

A = 200 * sqrt ( 2 )

A = 200 * 1.41421356

A = 282.842712 mm ^ 2

• Area Geometry - Anonymous, Thursday, April 11, 2013 at 3:18pm

Find the area of the shaded portion of the diagram (use 3.14 for p).

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