Find areas of regular polygons Find areas of circles

Find Areas of Regular Polygons

Apothem – a segment that is drawnFrom the center of a regular polygon Perpendicular to the side of the polygon.

If all radii were drawn, there would be 6 congruent isosceles triangles.

An area of a hexagon is determined by adding areas of the triangles inside.

AB

C

DE

F GH

P

Find the are of a regular pentagon with a perimeter of 40 cm.

K

L

MQN

J P

TAN angle MPQ = QM / PQTAN 36 = 4 / PQPQ = 4 / TAN 36PQ ~ 5.5½ (40)(5.5) = A~110So the area of the pentagon is about 110

centimeters.

Find Areas of Circles

Area of a circle = r²

48 in 34in

A caterer has a 48-inch diameter table that is 34 inches tall. She wants a tablecloth that will touch the floor. Find the area of the tablecloth.

34 + 48 + 34 = ll6 divided by 2 = 58 so the radius = 58.

A = pi(58)² ~ 10,568

Find the area of the shaded region. Assume that the triangle is equilateral.

4m

A = pi(4)²~ 50.3 – area of circle Use 30-60-90 rulesAB = 2BC = 2√3 DB = 2√3(√3) = 6A = ½ (4√3)(6)~20.8

50.3 – 20.8 =29.5 m²

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Thank you!

Laura Beth StoverConnor Reece