# The side of the isosceles triangle is 34, and the base is 60. Find the area of this triangle

May 31, 2020 | Education

| The area of any triangle is equal to half the product of the height and the side to which the height is drawn.

By the property of an isosceles triangle, BE is both height and median. Therefore, AE = EC = AC / 2.

The triangle ABE is rectangular (because BE is the height).

By the Pythagorean theorem, we find the height BE:

AB2 = AE2 + BE2

AB2 = (AC / 2) 2 + BE2

34 ^ 2 = (60/2) ^ 2 + BE ^ 2

1156 = 900 + BE ^ 2

BE ^ 2 = 256

BE = 16

SABC = (BE * AC) / 2 = (16 * 60) / 2 = 16 * 30 = 480

Answer: SABC = 480

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