4 Geometry Area and Perimeter

Tennessee Adult Education

Geometry – Area & PerimeterLesson 4

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. ©

Basic Shapes

Polygons are closed flat shapes with 3 or more

straight sides.

Quadrilaterals are polygons that have four sides and

four angles.

Name Shape Name ShapeTriangles

Parallelograms

Quadrilaterals RectanglesPentagon SquareHexagon RhombusOctagon Trapezoid

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.

•Example:

24 in.

10 in.

24 + 24 + 10 + 10 = 68 in.

Guided Practice

1. 2.

3. 4.

4 in 8 feet

3 feet

7 cm

5 cm

12 yards

Directions: Find the perimeter of each figure.

Guided Practice1. 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?

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

18 ft

Perimeter = 12+12+18+18

Perimeter = 60

60 x 12 = 720

720 ÷ 9 = 80 bricks

Area is the surface of a shape.

•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 = areacubic³ = volume

Who uses area in real life?Builders

Block layersCarpenters

LandscapersFloor layers

Area = Length x width (A = l x w)

Formula for Area of a Rectangle or Square

Each square equals one.

When finding the area of a surface, the answer must be in squared units. (inches, feet, miles, yards, etc.)

l = 6W = 5

A = l x wA = 6 x 5A = 30 units²

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?

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?

3. A piece a typing paper measures 11 inches by 8.5 inches. What is the area of a piece of this paper?

12 ft.

10 ft.A = L x wA = 12 x 10A = 120 ft.²

A = 300 ft²

93.5 in.²

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?

1. 32

2. 37

3. 420

4. 47

5. 57

20 ft

15 ft

10 ft

12 ft

Living Room

Dining Room

•"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

Area of a Triangle

HINT: The fraction line indicates division.

•

Example: What is the area of this triangle?

Hint: The fraction line means divide. Therefore, 240 ÷ 2 = 120

When solving for area, the units in the answer must be squared.

2

Guided PracticeFind the area of each triangle.

1.2.

3.

5 in. 8 in.

7 mm

3 in.

5 mm

6 in.

A = b x h 2A = 5 x 3 2A = 15 2A = 7.5 in.²

24 in.²

17.5 mm²

In the figure above, triangle ABC is an isosceles right triangle. What are the measures of its three angles?1. 30, 60, 902. 45, 45, 903. 60, 60, 604. 60, 90, 605. not enough information is given

A

B

CD

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

24 ft

30 ft

12 ft

Find the area, in square feet, of the figure above.

1. 1622. 2283. 2624. 3245. 396

Area = ½ x (base1 +base2) x height

Area = ½ x (30+24) x 12

Area = ½ x (54) x 12

Area = ½ x 648

Area = 324

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”.

How to find the circumference:

•

28 in

Area of a circle

•

6 in

²

HINT: 6² = 6 x 6

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?

2. The distance between the center and the edge of a circular race track is 3 miles. What is the distance around the track?

10 mi.

HINT: Remember the radius is half the diameter.

C = 18.84 miles A = 28.26 miles²

3. To the nearest foot, what is the circumference and the area of a circle swimming pool that has a radius of 6 feet?

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 = 37.68 feet A = 113.04 feet²

C = 47.1 cm A = 176.625 cm²