Geometry

Introduction to Perimeter, Circumference and Area

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 2

Goals:

• Find the perimeter and area of common plane figures.

• Use a general problem-solving plan.

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 3

Square

S

S

Perimeter

P = 4s

Area

A = s2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 4

Square Problem

Each side of a square measures 2.5 m. Find its perimeter and its area.

2.5 m

2.5 m

P = 4(2.5) = 10 m

A = 2.52 = 6.25 m2

Area is a square measure.

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 5

Rectangle

l

w

Perimeter

P = 2 l + 2w

Area

A = lw

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 6

Rectangle Problem

4 ft

2.1 ft

Find the perimeter and the area.

P = 2(4) + 2(2.1) = 8 + 4.2 = 12.2 ft

A = 4(2.1) = 8.4 ft2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 7

Triangle

h

b

a c

Perimeter

P = a + b + c

Area

bhA 21

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 8

Triangle Problem

3 in 8 in

10 in

2 in

Find the perimeter and the area.

P = 3 + 10 + 8 = 21 in

A = ½ (10)(2) = 10 in2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 9

Circle

rCircumference

C = 2r

Area

A = r2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 10

Circle Problem

If the diameter is 8, find the circumference and the area.8

r = 4

C = 2(4) = 8 25.13

(You could also use the formula C = d.)

A = (42) = 16 50.27

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 11

Problem Solving

1. Ask: What do I need to solve this problem? Draw a picture, if necessary, to help you determine this.

2. Label known and unknown facts.

3. Use labels and facts to choose related definitions, theorems, formulas, or other results you may need.

4. Reason logically to link the facts. Use a proof or other written argument.

5. Write a conclusion that answers the original problem. Check that your reasoning is correct.

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 12

Problem Solving Steps

1.Sketch2.Label3.Formulas4.Reason5.Conclusio

n6.Check

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 13

Problem 1A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?

1. Sketch

2. label

20 ft

30 ft.

A = ?

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 14

Problem 1 ContinuedA homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?

20 ft

30 ft.

A = ?

3. Formula: A = LW

a = 30(20) = 600 FT2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 15

Problem 1 ContinuedA homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?

20 ft

30 ft.

A = 600 FT2

4. Reason: Each bag covers 150 sq ft, and

he needs to cover 600 sq ft. 600 150

= 4

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 16

Problem 1 ConclusionA homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need?

20 ft

30 ft.

A = 600 FT2

5. Conclusion: He needs to buy 4 bags

of fertilizer.6. Check: 4 150 =

600

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 17

Problem 2You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat?

10

8

2

2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 18

Problem 2 ContinuedYou are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat?

Think: Larger mat, cut away the inside…

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 19

Problem 2 ContinuedYou are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat?

10

8

2

2

We need to know the area of the outer rectangle.12

14

Outer Area =

12 14 = 168

Inner Area =

8 10 = 80

Left over Area =

168 – 80 = 88 in2

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 20

Problem 3: You do it.You are making a triangular shaped window. The height of the window is 18 inches and the area will be 297 square inches. What will the length of the base of the window be?

18

b

b

b

b

bhA

33

9297

)18(297 21

21

The base will be 33 in.

April 20, 2023 Geometry 1.7 Perimeter, Circumference, Area 21

Homework