EXAMPLE 3 Find the area of an isosceles triangle

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Presentation transcript:

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 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.

Find the area of an isosceles triangle EXAMPLE 3 Find the area of an isosceles triangle Use the Pythagorean Theorem to find the height of the triangle. STEP 2 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.

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

GUIDED PRACTICE for Example 3 5. Find the area of the triangle. SOLUTION To find area of a triangle, first altitude has to be ascertained. 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.

GUIDED PRACTICE for Example 3 STEP 2 c2 = a2 + b2 182 = 152 + h2 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.

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

Find the area of the triangle. GUIDED PRACTICE for Example 3 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.

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