Section 9-4 Perimeter, Area, and Circumference

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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