In an isosceles triangle, the side is 13 cm, and the height drawn to the base is 5 cm. Find the area of this triangle.

| August 3, 2021 | education

Since in any isosceles triangle the height lowered to the base is at the same time the median, this height divides the base of the triangle in half.

Consider one of two identical right-angled triangles into which the height divides this isosceles triangle.

In this right-angled triangle, the hypotenuse is the lateral side of the isosceles triangle, and the legs are the height and half of the base of the isosceles triangle.

Using the Pythagorean theorem, we find the length of the leg equal to half the base of an isosceles triangle:

√ (13 ^ 2 – 5 ^ 2) = √ (169 – 25) = √144 = 12 cm.

Therefore, the base of this isosceles triangle is 3 * 12 = 24 cm

Knowing the base and the length of the height drawn to this base, we find the area of ​​the triangle:

24 * 5/2 = 5 * 24/2 = 5 * 12 = 60 cm ^ 2.

Answer: 60 cm ^ 2.



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