126 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Answer 10. 20 m2 Area of a Triangle The formula for the area of a triangle is given by read “one-half times base times height.” b h A 12 bh, The value of b is the measure of the base of the triangle. The value of h is the measure of the height of the triangle. The base b can be chosen as the length of any of the sides of the triangle. However, once you have chosen the base, the height must be measured as the shortest distance from the base to the opposite vertex (or point) of the triangle. Figure 2-7 shows the same triangle with different choices for the base. Figure 2-8 shows a situation in which the height must be drawn “outside” the triangle. In such a case, notice that the height is drawn down to an imaginary extension of the base line. Opposite vertex Finding the Area of a Triangle Base Find the area of the triangle. Solution: Identify the measure of the base and the height. Apply the formula for the area of a triangle. Write the whole numbers as fractions. Simplify. Multiply numerators. Multiply denominators. b 6 m and h 4 m 1 21 a6 3 1 12 1 mb a4 m2 12 m2 1 mb 1 2 a6 1 mb a4 1 mb 1 2 16 m2 14 m2 A 1 2 bh 4 m 6 m Example 6 Opposite vertex h h Base Base Opposite vertex h Figure 2-7 Figure 2-8 The area of the triangle is 12 square meters (m2). Skill Practice Find the area of the triangle. 10. 8 m 5 m
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