# The side of an isosceles triangle is 10, and the base is 12. Find the area of this triangle

May 31, 2020 | Education

| The area of the triangle is a * h / 2, where h is the height of the triangle, and is the side of the triangle to which the height is drawn.

SABC = AC * BD / 2

AD = DC = AC / 2 = 12/2 = 6 (by the property of an isosceles triangle, the height is the median)

Then, by the Pythagorean theorem:

AB2 = BD2 + AD2

10 ^ 2 = BD ^ 2 + 62

100 = BD ^ 2 + 36

BD ^ 2 = 64

BD = 8

SABC = AC * BD / 2 = 12 * 8/2 = 48

Answer: SABC = 48

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