Find the area of an isosceles triangle if the side is 10 and the base is 16.

From the condition it is known that an isosceles triangle is given by the length of the lateral side – 10 and base 16. And we need to find the area of the triangle.

To do this, apply the formula:

S = 1/2 * a * h_a.

The area of the triangle is equal to half the product of the side by the height dropped on it.

Find the length of the height by considering a right-angled triangle formed by the side of the triangle, half the base, and the height.

We are looking for height as an unknown leg according to the Pythagorean theorem:

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

b = √a ^ 2 – c ^ 2 = √ (10 ^ 2 – (16: 2) ^ 2) = √ (100 – 64) = √36 = 6.

S = 1/2 * 16 * 6 = 16 * 3 = 48 sq. units.