Geometry Introduction to Perimeter, Circumference and Area.

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.


Square

S

S

Perimeter

P = 4s

Area

A = s2


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.


Rectangle

l

w

Perimeter

P = 2 l + 2w

Area

A = lw


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


Triangle

h

b

a c

Perimeter

P = a + b + c

Area

bhA 21


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


Circle

rCircumference

C = 2r

Area

A = r2


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


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.


Problem Solving Steps

1.Sketch2.Label3.Formulas4.Reason5.Conclusio

n6.Check


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 = ?


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


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


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


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


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…


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


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.


Homework

Geometry Introduction to Perimeter, Circumference and Area.

Documents

Transcript of Geometry Introduction to Perimeter, Circumference and Area.