In an isosceles trapezoid, the side of the base is 10 cm 5 cm 15 cm, find the height of the trapezoid

An isosceles trapezoid is a trapezoid in which the sides are equal.

The height of the trapezoid is the perpendicular from the top of the obtuse angle to the large base:

BK and CN – trapezoid heights ABCD;

BK = CN.

The segment located between the perpendiculars of the tapes is equal to the length of its smaller base:

KN = BC = 5 cm.

Since the trapezoid is isosceles, then:

AK = ND.

In order to find the length of the segments AK and ND, you need:

AK = ND = (AD – KN) / 2;

AK = ND = (15 – 5) / 2 = 5 cm.

In order to find the length of the height BK, consider the triangle ΔABK. This triangle is rectangular. We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BK ^ 2 + AK ^ 2;

BK ^ 2 = AB ^ 2 – AK ^ 2;

BK ^ 2 = 10 ^ 2 – 5 ^ 2 = 100 – 25 = 75;

BK = √75 ≈ 8.66 cm.

Answer: the length of the height BK is 8.66 cm.