1.2.1 Using Formulas in Geometry Key Objectives • Apply formulas for perimeter, area, and circumference. Key Terms • The perimeter P of a plane figure is the sum of the side lengths of the figure. • The area A of a plane figure is the number of nonoverlapping square units of a given size that exactly cover the figure. • The base b of a triangle can be any side of the triangle. • The height h of a triangle is a segment from a vertex that forms a right angle with a line containing the base of the triangle. • In a circle, a diameter is a segment that passes through the center of the circle and whose endpoints are on the circle. • A radius of a circle is a segment whose endpoints are the center and a point on the circle. • The circumference of a circle is the distance around a circle. • Pi ( π ) is the ratio of a circle’s circumference to its diameter. Formulas • Perimeter of a Rectangle P = 2 l + 2 h , where l is the length and h is the height of the rectangle. • Area of a Rectangle A = lh , where l is the length and h is the height of the rectangle. • Perimeter of a Triangle P = a + b + c , where a , b , and c are the lengths of the sides of the triangle. • Area of a Triangle A = 1/2 bh , where b is the length of the base and h is the height of the triangle.
• Area of a Square A = s 2 , where s is the length of one side of the square. • Circumference of a Circle C = 2 πr , where r is the radius of the circle. • Area of a Circle A = πr 2 , where r is the radius of the circle. Example 1 Finding Perimeter and Area
The perimeter P of a plane figure is the sum of the side lengths of the figure. So, if a figure has five sides, then add the lengths of those five sides to find the figure’s perimeter. Multiplication can be used to find the perimeter of a figure when that figure has sides of equal length. For example, if the sides of a five-sided figure all have equal length s , then the perimeter of that figure is equal to s + s + s + s + s , or 5 s . The area A of a plane figure is the number of nonoverlapping square units of a given size that exactly cover the figure. Area can be visualized as the number of squares on a checkerboard. If a checkerboard has five squares across the top and nine squares on the side, then there are 5(9) or 45 squares on the board and 45 squares is the area of the checkerboard. In this lesson, the area of a rectangle, square, triangle, and circle will be found using given formulas.
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