The base of an isosceles trapezoid 12 and 24, perimeter = 56, find the area?

Since the trapezoid is isosceles, then AB =CD, then the perimeter of the trapezoid is:

Ravsd = 2 * AB + BC + AD.

56 = 2 * AB + 12 + 24.

2 * AB = 56 – 36 = 20.

AB = СD = 20/2 = 10 cm.

Let’s build the height of the HВ.

Since the trapezoid is isosceles, the BH height divides the larger base into two segments, the length of the smaller of which is equal to the half difference of the base lengths.

AH = (AD – BC) / 2 = (24 – 12) / 2 = 6 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 100 – 36 = 64. BH = 8 cm.

Determine the area of the trapezoid.

Savsd = (ВС + AD) * ВН / 2 = (12 + 24) * 8/2 = 144 cm2.

Answer: The area of the trapezoid is 144 cm2.