The Apothem The apothem a is the segment

The Apothem The apothem (a) is the segment drawn from the center of the polygon to the midpoint of the side (and perpendicular to the side)

Deriving the Formula - Squares The diagonals of the square divide it into four triangles with base s and height a. The area of each triangle is sa. Since there are 4 triangles, the total area is 4( )sa or (4 s)a. Since the perimeter (p) = 4 s the formula becomes A = ap

Deriving the Formula - Triangles Connecting the center of the equilateral triangle to each vertex creates three congruent triangles with area A = sa. Since there are three triangles, the total area is 3( )sa, or (3 s)a. Since the perimeter = 3 s, the formula may be written A = ap

Deriving the Formula - Regular Hexagons Connecting the center of the regular hexagon to each vertex creates six congruent triangles with area A = sa. Since there are six triangles, the total area is 6( )sa, or (6 s)a. Since the perimeter = 6 s, the formula may be written A = ap

Finding the apothem - Square The apothem of a square is one-half the length of the side. If as == 14, 15, sa == ? ? If a = 7. 5 s = 28

Find the apothem - Triangles The apothem of an equilateral triangle is the short leg of a 3060 -90 triangle where s/2 is the long leg. 60 30 Then a = (s/2)/ 3 90 or

Find the apothem - Triangles If. If s. If=ss 10, ==24, 18, a =aa? == ? ?

Find the side - Triangles If If the apothem is is 6 cm, the side = ? 2. 5 cm, the side = ?

Finding the apothem - Hexagons The apothem of a regular hexagon is the long leg of a 30 -60 -90 triangle. 30 60 Therefore, the apothem is (s/2) 90

Finding the apothem - hexagons If the side = 5 If the side = 12 the apothem = ?

Finding the side - hexagons If If the apothem == 16, 12, the side == ? ?

Finding the area - Squares a = 6 cm Find the area 2 A = 144 cm 2 2 AA= =50 cm 288 cm

Finding the Area - Triangles If a = 3 cm, find the area of the triangle

Finding the Area - Triangles If a = 5 cm, find the area of the triangle

Finding the Area - Triangles

Finding the Area - Triangles If the side of the triangle = 10 cm, find the area of the triangle

Finding the Area - Triangles

Finding the area - hexagons If the a = 6 cm, find the area of the hexagon.

Finding the area - hexagons

Finding the area - hexagons

Finding the area - hexagons