What is the area of an isosceles triangle if its base is 120 m and its lateral side is 100 m?

Let us drop the height from the vertex of this isosceles triangle to its base.

Let’s find the length of this height.

It is known that in any isosceles triangle, the height lowered to its base divides this base in half.

Therefore, we can find the length of the height h of a given isosceles triangle using the Pythagorean theorem:

h = √ (100 ^ 2 – (120/2) ^ 2) = √ (100 ^ 2 – 60 ^ 2) = √ (10000 – 3600) = √6400 = 80 m.

Knowing the length of the height and base, we find the area S of this triangle:

S = 120 * 80/2 = 120 * 40 = 4800 m ^ 2.

Answer: the area of the triangle is 4800 m ^ 2.