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EXAMPLE 3

STEP 1. Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown. EXAMPLE 3.

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EXAMPLE 3

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  1. STEP 1 Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown. EXAMPLE 3 Find the area of an isosceles triangle Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. SOLUTION

  2. STEP 2 Use the Pythagorean Theorem to find the height of the triangle. EXAMPLE 3 Find the area of an isosceles triangle c2 = a2 + b2 Pythagorean Theorem 132 = 52 + h2 Substitute. 169 = 25 + h2 Multiply. 144 = h2 Subtract 25 from each side. 12 = h Find the positive square root.

  3. (base) (height) = (10) (12) = 60 m2 ANSWER The area of the triangle is 60 square meters. 1 1 2 2 EXAMPLE 3 Find the area of an isosceles triangle STEP 3 Find the area. Area =

  4. STEP 1 By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles. for Example 3 GUIDED PRACTICE 5. Find the area of the triangle. SOLUTION To find area of a triangle, first altitude has to be ascertained.

  5. for Example 3 GUIDED PRACTICE STEP 2 c2 = a2 + b2 Pythagorean Theorem 182 = 152 + h2 Substitute. 324 = 225 + h2 Multiply. 99 = h2 Subtract 225 from each side. 9.95 = h Find the positive square root.

  6. (base) (height) = 30 9.95 = 149.25 ft2 ANSWER The area of the triangle is 149.25 ft2. 1 1 2 2 for Example 3 GUIDED PRACTICE STEP 3 Find the area. Area =

  7. for Example 3 GUIDED PRACTICE 6. Find the area of the triangle. SOLUTION c2 = a2 + b2 Pythagorean Theorem 262 = 102 + h2 Substitute. 676 = 100 + h2 Multiply. 576 = h2 Subtract 100 from each side. 24 = h Find the positive square root.

  8. ANSWER The area of the triangle is 240 square meters. 1 1 2 2 for Example 3 GUIDED PRACTICE Area = (base) (height) = (20) (24) = 240 m2

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