# The side of an isosceles triangle is 35 and the base is 42. Find the area of this triangle.

July 28, 2021 | education

| Given: △ GHK – isosceles, GH = KH = 35 cm, GK = 42 cm.

Find: S △ GHK.

In order to find the area of an isosceles H GHK, it is necessary to draw the height HF from the top of H to the bottom of GK.

From the properties of an isosceles triangle, it is known that the height drawn from the apex of a given triangle to the base is also its median and bisector.

The median divides the side in half (a property of the medians). Means:

FK = 1/2 * GK = 1/2 * 42 = 21 (cm).

△ HFK – rectangular (∠F = 90 °). Behind the Pythagorean theorem:

KH2 = FK2 + HF2.

Hence:

HF2 = KH2 – FK2 = 352 – 212 = 1225 – 441 = 784 (cm),

HF = Sqrt784 = 28 (cm).

Now we find the area △ GHK:

S △ GHK = 1/2 * GK * HF = 1/2 * 42 * 28 = 588 (cm2).

Answer: S △ GHK = 588 cm2.

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