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In the diagram, O is the center of a circle with radii OP=OQ=\(20\). What is the perimeter of the shaded region?

Guest Apr 6, 2022

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Best Answer

Since there are 360^o in a circle and a 90^o sector has been removed, 270^o remain.

Therefore, you want 270^o / 360^o, or 3/4^ths of the circumference (plus the two radii).

The formula for the circumference of a circle is: 2·pi·radius.

[ (3/4) · (2·pi·20) ] + [ 2·20 ] = the perimeter of the shaded region

geno3141 Apr 6, 2022

geno3141 · Answer 1 · 2022-04-06T06:05:59

Since there are 360^o in a circle and a 90^o sector has been removed, 270^o remain.

Therefore, you want 270^o / 360^o, or 3/4^ths of the circumference (plus the two radii).

The formula for the circumference of a circle is: 2·pi·radius.

[ (3/4) · (2·pi·20) ] + [ 2·20 ] = the perimeter of the shaded region