In an isosceles triangle, the side is 10 inches and the base is 12 cm.

In an isosceles triangle, the side is 10 inches and the base is 12 cm. Find: a) the height of the triangle drawn to the base of the triangle; b) the area of the triangle.

Given a triangle ABC, BD = h – the height of the triangle to the base, AB = BC = 10 cm.Then the height drawn to the base of the isosceles triangle ABC divides this base in half, that is, CD = AC / 2 = 6 cm.
a) Consider a triangle BDC – right-angled. Then the side BD = h can be found by the Pythagorean theorem:
BD ^ 2 = h ^ 2 = BC ^ 2 – CD ^ 2 = 100 – 36 = 64 cm ^ 2.
Then the height is h = 8 cm.
b) The area of the triangle is calculated by the formula:
S = ½ * AC * h = ½ * 12 * 8 = 48 cm ^ 2.