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Name: _________________________________________ Date: _________________

Lessons 3-8, 10-6, and 10-7: Perimeter, Area, and Circumference

What is the perimeter of a shape?

Perimeter of Rectangles and Squares

Perimeter of a Rectangle: Perimeter of a Square: [pic]

What is the perimeter of a circle called? _________________

Circle – the set of all points in a plane that are the _________ _____________ from a given point (called the center of the circle).

What is the relationship between the diameter and the radius of a circle?

Circumference of Circles

Circumference of a Circle: [pic]

Do you know another way to write this formula using diameter?

Exercises:

State the diameter and radius of each of the following circles.

[pic] [pic] [pic]

What is the area of a shape?

|Shape |Area Formula |Model |

| | |[pic] |

|Rectangle |[pic] | |

| | |[pic] |

|Square |A = _______ | |

| | |[pic] |

|Parallelogram |[pic] | |

| | |[pic] |

|Triangle |[pic] | |

| | |[pic] |

|Trapezoid |[pic] | |

|a trapezoid has ______ pair of ___________ sides | | |

| | |[pic] |

|Circle |[pic] | |

[pic]

Exercises:

Find the perimeter and area of each rectangle. Show your work.

1) 2)

[pic] [pic]

3) 4)

5) Find the perimeter and area of a square with side length 5 inches.

Exercises:

Find the area of each figure.

6) 7)

8) 9)

10) 11)

3 m 5.5 m

13 m

8 km

12) 13)

9 km 8 km 10 km

20 km

Exercises:

Find the circumference and area of each circle. Use calculator π. Round to the nearest tenth.

14) 15)

C [pic] ___________ C [pic] ____________

A [pic] ___________ A [pic] ____________

16) 17)

C [pic] ___________ C [pic] ____________

A [pic] ___________ A [pic] ____________

Find the missing dimension of each of the following.

18) 19)

l

w [pic] w = 84 in [pic] w = 21 m

15 m

20) 21)

Perimeter = 55 m w

w

22) Area = 14.7 m2 23) 6.5 in Area = 19.5 in2

h = ? h = ?

7 m 3.25 in

24) The perimeter of a rectangle is 100 centimeters. 25) The area of a rectangle is 319 square

Its width is 9 centimeters. Find its length. kilometers. Its width is 11 kilometers. Find its

length.

26) Suppose a triangle has an area of 220 square meters. 27) A trapezoid has an area of 27.5 square

What is the measure of the height if the base measures centimeters. What is the measure of the height

20 meters? if the bases measure 7 centimeters and 4

4 centimeters?

28) Find the base of a parallelogram with a height of 29) The circumference of a circle is about 15.71

10.5 feet and an area of 189 square feet. inches. What is the diameter of the circle?

30) The circumference of a circle is about 100.53 31) The area of a circle is about 201.0619. What

meters. What is the radius of the circle? is the radius of the circle?

32) In bowling, the distance from the foul line 33) A carousel has a diameter of 40 feet. How far

to the head pin is 60 feet. A bowling ball has does the carousel travel in 12 revolutions?

a radius of about 4.3 inches. How many times

must the ball rotate in order to strike the headpin?

34) Mrs. Humphrey needs to replace a broken window at her house. The window is shaped like a trapezoid

with the dimensions shown below. If the glass costs $4.50 per square foot, how much will the replacement

window cost?

EXTRA CHALLENGE!

35) Thomas would like to fence in his rectangular 36) Anjelica’s family is putting a walkway around

yard for his dog. If the yard measures 24 feet their pool. If the dimensions of the pool are

by 18 feet, how many yards of fencing are needed 20 feet by 12 feet, and they want the walkway

to enclose the yard? to extend three feet on each side of the pool,

what will be the area of the walkway?

Area of walkway = area of __________________ - area of _____________

[pic]

Semicircle - ___________ of a circle.

Area of a semicircle = __________[pic]

Exercises:

Find the area of each of the following semicircles. Use calculator π. Round to the nearest tenth.

37) 38) 39) 40)

Summary

[pic]

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[pic]

FORMULA SUBSTITUTE SOLVE

It does not matter which dimension is the length and which dimension is the width!

Note the labels!

Jyles’ backyard is shaped like the parallelogram above. He would like to put new sod (grass) in his yard. If it costs $12.50 per square yard, how much will it cost to sod his yard?

How do you find the area of a quarter circle?

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