Area Unit 10 Area of Regular Polygons the

Area Unit 10

Area of Regular Polygons � the sum of all the degrees at the center of any polygon is 360° � for any regular polygon, divide 360° by the number of sides of the polygon, to find the measure of the angle at the center.

Area of Regular Polygons

Area of Regular Polygons

Area of Regular Polygons

Apothems: 1. All apothems of a regular polygon are congruent. 2. Only regular polygons have apothems. 3. An apothem is a radius of a circle inscribed in the polygon. 4. An apothem is the perpendicular bisector of a side. 5. A radius of a regular polygon is a radius of a circle circumscribed about the polygon. 6. A radius of a regular polygon bisects an angle of the polygon.

Area of Regular Polygons

A regular polygon has a perimeter of 40 cm and an apothem of 5 cm. Find the polygon’s area. A = ½ap = ½(5)(40) = 100 cm 2

Find the are of the regular polygon.

Example 4: Find the area of a regular pentagon with 7. 2 ft sides p = ns and a 6. 1 ft radius. = (5)(7. 2 ft) A = ½ ap = 36 ft = ½ (4. 92 ft)(36 ft) = 88. 6 ft 2 6. 1 ft a 2 + b 2 = c 2 a 2 + 3. 62 = 6. 12 3. 6 ft a 2 + 12. 96 = 37. 21 a 2 = 24. 25 a = 4. 92

Find the area of a regular hexagon whose sides are 18 cm long. 1. Draw the picture 2. Write the formula 3. Plug in the numbers 4. Solve and label units

Find the perimeter Find each angle Find the apothem P = 18(6) = 108 cm 18 cm Angles = 720º/6 angles = 120º per angle Write the formula, and Radius breaks it into 60º angles. 30 -60 -90 triangle, apothem = solve. 9√ 3 cm A = ½ ap A = ½ (9√ 3)108 2 A = 486√ 3 cm

Area of Regular Polygons