What is the area of a triangle if its sides are 5 cm 5 cm and 5 cm?

Let triangle ABC be equilateral, i.e.

AB = BC = AC = a.

Since all angles of this triangle are equal, then all angles are equal

180 ° / 3 = 60 °.

Let us drop the height BM from the top B to the bottom AC.

Consider a right-angled triangle ABM.

Then BM = AB * cos (BAC) = a * sin (60 °) = a * √3 / 2.

Area ABC = 1/2 * AC * BM = 1/2 * a * a * √3 / 2 =

= (a ^ 2 * √3) / 4.

Therefore, in our case, the area is equal to:

(5 * 5 * √3) / 4 = (25 * √3) / 4.