1. Section 9-4
Perimeter, Area, and Circumference

2. Perimeter, Area, and Circumference
Perimeter of a Polygon
Area of a Polygon
Circumference of a Circle
Area of a Circle

3. Perimeter of a Polygon
The perimeter of any polygon is the sum of the measures of the line segments that form its sides. Perimeter is measured in linear units.

4. Perimeter of a Triangle
The perimeter P of a triangle with sides of lengths a, b, and c is given by the formula
P = a + b + c. b a c

5. Perimeter of a Rectangle
The perimeter P of a rectangle with length l and width w is given by the formula
P = 2l + 2w,
or equivalently
P = 2(l + w). l w

6. Perimeter of a Square s s
The perimeter P of a square with all sides of length s is given by the formula
P = 4s. s s

7. Area of a Polygon
The amount of plane surface covered by a polygon is called its area. Area is measured in square units.

8. Area of a Rectangle
The area A of a rectangle with length l and width w is given by the formula
A = lw. l w

9. Example: Rectangle Solution
Find the perimeter and area of the rectangle below.
15 ft.
Solution
7 ft.
Perimeter
P = 2l + 2w = 2(15) + 2(7) = 44 ft.
Area
A = lw = 15(7) = 105 ft.2

10. Area of a Square
The area A of a square with all sides of length s is given by the formula
A = s2. s s

11. Area of a Parallelogram
The area A of a parallelogram with height h and base b is given by the formula
A = bh. h b

12. Area of a Trapezoid
The area A of a trapezoid with parallel bases b and B and height h is given by the formula b h B

13. Example: Area of a Parallelogram
Find the area of the trapezoid below.
7 cm.
5 cm.
Solution
13 cm.

14. Area of a Triangle
The area A of a triangle with base b and height h is given by the formula h b

15. Example: Area With Multiple Shapes
Find the area of the shaded region below.
4 in.
Solution
4 in.
Area of square – Area of triangle

16. Circumference of a Circle
The distance around a circle is called its circumference.

17. Circumference of a Circle
The circumference C of a circle of diameter d is given by the formula.
or equivalently r d
where r is a radius.

18. Area of a Circle
The area A of a circle with radius r is given by the formula. r

19. Example: Circle Solution
Find the area and circumference of a circle with a radius that is 6 inches long (use 3.14 as an approximation for pi).
Solution
Circumference
Area