This document provides information and formulas for calculating the perimeter and area of various polygons. It includes formulas for finding the perimeter and area of rectangles, parallelograms, triangles, trapezoids, rhombi, kites, and regular polygons. The key points are that perimeter is found by adding all the sides of any polygon, and area formulas vary depending on the specific shape but generally involve multiplying base and height or base and apothem.

1. Jim Smith
JCHS
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.
PERIMETER AND AREA OF POLYGONS

2. PERIMETER
There are many formulas
(or shortcuts) for finding the
perimeter of polygons. The only
one you need to remember is….
ADD ALL SIDES
This will work for all polygons

3. 8
8
8
3 3
9
9
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

4. Area of Rectangles
Think of filling the rectangle with boxes.
All answers should be in square units.
4
3
4 Columns
By 3 Rows
4X3= 12
This is the length
times the width
A= lw

5. 5
51
38
12
A=lw
A=51x5
A=255 sq units
A=lw
A=38x12
A=456 sq units
Rectangles

6. Area of Parallelograms
h
b
A=bh
The height must
form a right angle
with a base
h
b

7. 7
10
15
6
A=bh
A=10x7
A=70 sq. units
A=bh
A=15x6
A=90 sq. units
Parallelograms

8. Area of Triangles
b b
h h
A=1/2 bh

9. Triangles
21
7
A = ½ bh
A = ½ 7x21
A = ½ 147
A = 147
2
A = 73½
A = 73.5 sq units

10. Right Triangle Equilateral or
Isosceles Triangle
6
8
A = ½ bh
A = ½ 6 x 8
A = 24 Sq. Unit
10 10
10
60° 60°
60°
5 5
5√3
A = ½ bh
A = ½ 10 x 5√3
A = 25√3 Sq. Unit

11. Area of Trapezoids
b1
b2
h
A = ½ h( b1 + b2 )

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

13. 45°
8
14
8 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

14. 60°
6
16
6
5 5
60°
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

15. Area of Rhombi
and Kites
d1
d2
A = ½ d1 x d2
d2
d1
( d1 and d2 are the whole diagonals )

16. Rhombus and Kite
10
8
X
6
8
6
A = ½ d1 x d2
A = ½ 12x16
A = 96 sq units
4
3 7
4
A = ½ d1 x d2
A = ½ 8x10
A = 40 sq units

17. Area of Regular Polygons
s
r
a
s = side
a = apothem
r = radius
A=1/2 aP

18. 6
5
3 3
4 3²+x² = 5²
A = ½ aP
A = ½ 4x36
A = 72 sq units
P = 6x6
P = 36
Regular Hexagon

19. The area of any figure is the sum of
all the non-overlapping parts
Trapezoid
Triangle
Rectangle

20. + + +
Add The Parts
OR

21. Complete the figure and subtract the
part you don’t want ( bake the cake
and eat the part you don’t want! )