Find the area of an isosceles triangle, the side of which is 15 cm, and the base is 24 s.

To calculate the area of ​​an isosceles triangle, we use the formula:

S = 1/2 * a * ha.

The area of ​​an isosceles triangle is equal to half the product of the base by the height dropped on it.

From the condition, we know the lateral side – 15 cm, as well as the length of the base 24 cm.

We need to find the height. The height in an isosceles triangle is also the median (divide the base into two equal parts).

Consider the height as a leg of a right-angled triangle formed by the side (hypotenuse) and half of the base:

24: 2 = 12 cm.

Let’s apply the Pythagorean theorem:

c ^ 2 = a ^ 2 + b ^ 2;

a = √ (c ^ 2 – b ^ 2) = √ (15 ^ 2 – 12 ^ 2) = √ (225 – 144) = √81 = 9 cm.

Let’s calculate the area:

S = 1/2 * 24 * 9 = 108 cm ^ 2.