In an isosceles trapezoid, the bases are 10 cm and 40 cm. The lateral side is 25 cm.

In an isosceles trapezoid, the bases are 10 cm and 40 cm. The lateral side is 25 cm. Calculate the height of the trapezoid.

The height of the trapezoid dropped to the base is H, the side of the trapezoid is c = 25 cm, and half of the difference between the bases (a – b) / 2 is a right-angled triangle. In this triangle, c is the hypotenuse, and H and (a – b) / 2 – legs.

Let’s apply the Pythagorean theorem for the sides of this triangle.

c ^ 2 = H ^ 2 + [(a – b) / 2] ^ 2;

First, we define a and b; (a – c).

(a – c) / 2 = (40 – 10) / 2 = 15 (cm);

we write down the equality of Pythagoras:

25 ^ 2 = H ^ 2 + 15 ^ 2;. H ^ 2 = 625 – 225 = 400;

Determine the height of the trapezoid:

H = √ (40) = 20 (cm).