In an isosceles triangle, the height to the base is 8 cm, the side is 10 cm. Find the perimeter and area of the triangle.

1) According to the Pythagorean theorem, the square of half of the base can be found as the difference between the squares of the side and the height drawn to the base:

102 – 82 = 100 – 64 = 36 = 62;

This means that half of the base is 6 cm, respectively, the base of this isosceles triangle is 12 cm.

2) We find the perimeter as the sum of the lengths of the two lateral sides and the base: P = 10 + 10 + 12 = 32 cm.

3) We find the area of the triangle as half of the product of the base and the height drawn to it: S = 0.5 * 12 * 8 = 48 cm2.