Find the length of the side of an isosceles trapezoid when the length of its base is equal to 9 cm

Find the length of the side of an isosceles trapezoid when the length of its base is equal to 9 cm and 21 cm, and the area is exactly 120 cm2.

The area of ​​any trapezoid can be found by the formula:

S = 1 / 2h * (a + b), where h is the height of the trapezoid, and a and b are its base.

Let’s lower the height from the smaller base to the larger one. This height, the side of the trapezoid and the segment that separates its height from the larger base of the trapezoid form a right-angled triangle between them. Since the trapezoid is isosceles, the segment mentioned last can be found by the following formula:

c = (b – a) / 2.

Let’s find this segment:

c = (21 – 9) / 2 = 12/2 = 6 cm.

From the area formula, we express the height:

h = 2S / (a ​​+ b).

Find the height:

h = 2 * 120 / (9 + 21) = 240/30 = 8 cm.

In the previously considered right-angled triangle, the side of the trapezoid is the hypotenuse, so it can be found by the Pythagorean theorem. Let’s find it:

√ (6² + 8²) = √ (36 + 64) = √100 = 10 cm.

Answer: the side of an isosceles trapezoid is 10 cm.