Jim SmithJCHS

3108.1.9    Expand analysis of units of measure to include area and volume.

3108.4.27  Use right triangle trigonometry to find the area and perimeter of quadrilaterals

  3108.4.28  Derive and use the formulas for the area and perimeter of a regular polygon. 

PERIMETERThere are many formulas

(or shortcuts) for finding theperimeter of polygons. The only one you need to remember is….

ADD ALL SIDESThis will work for all polygons

8

88

3 3

99

4

13

7

5

4

7

4

5

4

7

P= 3+8+3+8=22 P= 4+5+5+4+7=25

P= 9+9+4=22

P= 13+7+4+7=31

Area of RectanglesThink of filling the rectangle with boxes. All answers should be in square units.

4

3

4 ColumnsBy 3 Rows

4X3= 12This is the lengthtimes the width

A= lw

551

38

12A=lw

A=51x5A=255 sq units

A=lwA=38x12

A=456 sq units

Rectangles

Area of Parallelograms

h

b

A=bh

The height must form a right anglewith a base

7

10

15

6

A=bhA=10x7

A=70 sq. units

A=bhA=15x6

A=90 sq. units

Parallelograms

Area of Triangles

b b

h h

A=1/2 bh

Triangles

21

7

A = ½ bhA = ½ 7x21A = ½ 147

A = 147 2A = 73½A = 73.5 sq units

Right Triangle Equilateral orIsosceles Triangle

6

8

A = ½ bhA = ½ 6 x 8A = 24 Sq. Unit

10 10

1060° 60°

60°

5 5

5√3

A = ½ bhA = ½ 10 x 5√3A = 25√3 Sq. Unit

Area of Trapezoidsb1

b2

h

A = ½ h( b1 + b2 )

8

6

12A = ½ h(b1 + b2)A = ½ (6)( 8+12 )A = 3( 20 )A = 60 sq units

Trapezoid

45°

8

148 6

6

A = ½ h(b1 + b2)A = ½ 6( 8+14 )A = ½ 6(22)A = 66 sq units

Trapezoid with 45°

45°

6

60°

6

166

5 560°5√3

5

A=1/2 h( b1+b2 )A= ½ 5√3 ( 6+16 )A= ½ 5√3 ( 22 )A= 5√3 ( 11 )A= 55√3 sq units

Isosceles Trapezoid

Area of Rhombiand Kites

d1 d2

A = ½ d1 x d2

d2

d1

( d1 and d2 are the whole diagonals )

Rhombus and Kite

108X6

8 6

A = ½ d1 x d2

A = ½ 12x16A = 96 sq units

43 7

4

A = ½ d1 x d2

A = ½ 8x10A = 40 sq units

Area of Regular Polygons

s

r

a

s = sidea = apothemr = radius

A=1/2 aP

6

5

3 3

4 3²+x² = 5²

A = ½ aPA = ½ 4x36A = 72 sq units

P = 6x6P = 36

Regular Hexagon

The area of any figure is the sum of all the non-overlapping parts

Trapezoid

Triangle

Rectangle

+ + +Add The Parts

OR

Complete the figure and subtract thepart you don’t want ( bake the cakeand eat the part you don’t want! )