Perimeter of Polygons

Perimeter

Warm-Up

In a rectangle, the length is 4 meters longer than the width. If the perimeter is 84 meters, find the length and the width.

Vocabulary

44) Perimeter

45) Circumference

Perimeter of Polygons

The distance around a two-dimensional object is called its perimeter. To find the perimeter, you must add up the lengths of all the outer edges of a plane figure. Do not include any inner edges, such as diagonals, and make sure you include all the sides in your calculation.

Examples

1 2 Common Formulas to Memorize

Perimeter = 2L + 2W Perimeter = 4s

Exercise

3 Algebraic Expressions of Perimeter

Model Problems

1) The second side of a triangle is one less than the length of the first side, and the third side is twice the length of the second side. Write an expression to describe the perimeter of the triangle.

4 2) One side of a square is represented by the expression n – 4. What is the perimeter of the square in terms of n?

3) The length of a rectangle is 2 less than three times the width. If the perimeter of the rectangle is 76, find the length and the width of the rectangle.

5 Exercise

1) The perimeter of the triangle below is 34 yards. Find the length of each side.

2) Express, in terms of n, the perimeter of a regular pentagon whose side measures 2n -1.

3) Express the perimeter of the rectangle at right in terms of x:

Circumference of Circles and Semicircles

The circumference of a circle is the distance around the circle.

The formula for circumference is:

Circumference = π (C = π d)

Circumference = (C = 2 π r)

A semicircle is half a circle. The distance around a semicircle is half the circumference plus the length of the diameter:

Circumference =

6 Model Problems Find the circumference. Express the answer in terms of π and to the nearest tenth.

Exercise Find the circumference of each figure in terms of π and to the nearest tenth.

7 Perimeter of Composite Figures

Model Problems Find the perimeter of each figure. Express answers in terms of π and to the nearest tenth where appropriate.

Exercises Find the perimeter of each figure. Express answers in terms of π and to the nearest tenth where appropriate.

8 Homework

1) Write each formula 5 more times.

Perimeter of a Rectangle Perimeter of a Square Circumference of a Circle P = 2L + 2W P = 4s C = or

2) Find the perimeter or circumference.

9 5) A semicircle with radius = 7