The side of an isosceles triangle is 17 cm and the base is 30 cm. Find the height drawn to the base and the area of the triangle.

The area of a triangle is calculated using the formula: S = 0.5 * AC * BH.
To find BH, consider a right-angled triangle ABH. The height BH divides the AC side in half, so AH = AC: 2 = 30: 2 = 15.
AB ^ 2 + AH ^ 2 = BH ^ 2;
BH = √ (AB ^ 2 – AH ^ 2) = √ (17 ^ 2 – 15 ^ 2) = √64 = 8.
S = 0.5 * 30 * 8 = 120 cm ^ 2.
Answer: The height of the triangle, drawn to the base, is 8 cm, the area of the triangle is 120 cm ^ 2.