This document provides instruction on calculating the perimeter and area of basic shapes like triangles, rectangles, squares and circles. It defines key terms, provides formulas and examples for finding perimeter and area. Step-by-step worked examples are included to demonstrate calculating perimeter and area of different shapes.

1. Geometry – Area & Perimeter
Lesson 4
Tennessee
Adult Education
This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

2. Basic Shapes
Polygons Quadrilaterals
are closed flat shapes with 3 or more are polygons that have four sides and
straight sides. four angles.
Name Shape Name Shape
Triangles Parallelograms
Quadrilaterals Rectangles
Pentagon Square
Hexagon Rhombus
Octagon Trapezoid

3. Finding the Perimeter
•The perimeter is the distance around a figure such as a square,
a rectangle, or a triangle.
– To find the perimeter of a figure, you simply add
up all the sides.
24 in.
•Example:
10 in.
24 + 24 + 10 + 10 = 68 in.

4. Directions: Find the perimeter of each
Guided Practice figure.
4 in 8 feet
1. 2. 3 feet
12 yards
7 cm
3. 4.
5 cm

5. Guided Practice
1. How many feet of fencing material will Sarah need to surround
her garden that measures 10 feet on two sides and 5 feet on
the other two sides?

6. The illustration shows the dimensions of a vegetable garden in the Reed’s backyard. Mr.
Reed wants to lay 9-inch-long bricks end to end around the garden. Find the minimum
number of bricks that are required to surround the garden.
1. 50
2. 60
3. 70
4. 80
12 ft
Perimeter = 12+12+18+18
Perimeter = 60 18 ft
60 x 12 = 720
720 ÷ 9 = 80 bricks

7. Area is the surface of a shape.
Who uses area in real life?
Builders
Block layers
Carpenters
Landscapers
Floor layers
•Ex. A wall has a surface. To find the area of a wall is to find the entire
size of the wall. This would help to find out how much paint to buy if
you were painting the wall, or how many bricks you need to complete
the wall.
•On the GED test if a questions asks for:
squared² = area
cubic³ = volume

8. Formula for Area of a Rectangle or Square
Area = Length x width (A = l x w)
Each square equals one.
l = 6
W = 5
A = l x w
A=6x5
A = 30 units²
When finding the area of a surface, the answer must
be in squared units. (inches, feet, miles, yards, etc.)

9. Guided Practice
1. Frenda found that a bedroom floor measures 12 feet
long and 10 feet wide. How many square feet of
carpet will she need to buy to cover this floor?
10 ft.
A=Lxw 12 ft.
A = 12 x 10
A = 120 ft.²
2. If a room needs new tile and its measurements are 20
feet by 15 feet, how many square feet of tile will I
have to purchase?
A = 300 ft²
3. A piece a typing paper measures 11 inches by 8.5
inches. What is the area of a piece of this paper?
93.5 in.²

10. The diagram shows the floor plan of the living room and the dining room of the Reed’s
home. Rounded to the nearest square feet, what is the combined floor area of the two
rooms?
20 ft
1. 32
2. 37 Living
3. 420 15 ft Room
4. 47
5. 57
Dining
Room
10 ft
12 ft

11. Area of a Triangle
•"b" is the distance along the base of
the triangle
•"h" is the height (measured at right
angles to the base)
Area = base x height
2
Area = bh
2
HINT: The fraction line
indicates division.

12. Example: What is the area of this triangle?
Hint: The fraction line means divide.
Therefore, 240 2 = 120
2
When solving for area, the units in the answer must be squared .

13. Guided Practice
Find the area of each triangle.
2.
1. 3 in. 24 in.²
6 in.
5 in. 8 in.
A=bxh
2
A=5x3
3.
2
A = 15 5 mm
2
A = 7.5 in.² 17.5 mm²
7 mm

14. A
B
D
C
In the figure above, triangle ABC is an isosceles right triangle. What
are the measures of its three angles?
1. 30, 60, 90
2. 45, 45, 90
3. 60, 60, 60
4. 60, 90, 60
5. not enough information is given

15. Two angles of a triangle measure 36 and 44. Which expression could
be used to find the measure of the third angle?
1. 36+44+180
2. 36+ (44-180)
3. 180 – (36+44)
4. 180 – (36-44)
5. 90-36-44

16. 24 ft
Area = ½ x (base1 +base2) x height
Area = ½ x (30+24) x 12
12 ft Area = ½ x (54) x 12
Area = ½ x 648
Area = 324
30 ft
Find the area, in square feet, of the figure above.
1. 162
2. 228
3. 262
4. 324
5. 396

17. Circumference: the perimeter around a circle.
•Key terms:
•Diameter – is the distance across the circle. The symbol for
diameter is “d”.
•Radius – All the points on the outside of the circle are equal
distances from the center of a circle. The symbol for the radius is
“r”.

18. How to find the circumference:
28 in

19. Area of a circle
HINT: 6² = 6 x 6 6 in
²

20. Let’s Practice: Find the circumference & area of
each.
1. Garrett Refuge for Exotic Animals is in the shape of a circle.
If the distance across the property is 10 miles, what is its
circumference and area?
HINT: Remember the
radius is half the
10 mi. diameter.
2. The distance between the center and the edge of a circular
race track is 3 miles. What is the distance around the track?
C = 18.84 miles A = 28.26 miles²

21. 3. To the nearest foot, what is the circumference and
the area of a circle swimming pool that has a radius
of 6 feet?
C = 37.68 feet A = 113.04 feet²
4. Lil measured the widest distance across the top of a
circular can to be 15 centimeters. What is the
distance around the rim of the can, and what is its
area?
C = 47.1 cm A = 176.625 cm²