Find the area of an isosceles trapezoid if its bases are 8 and 12 cm. And the lateral side is 10 cm.

Isosceles is a trapezoid in which the sides are of equal length. The area of the trapezoid is the product of half of the sum of its bases by the height:

S = (ВС + АD) / 2 h.

Let’s find the height. Since the trapezoid is isosceles, the segments AH and KD, formed by the heights, are equal to each other:

AH = KD = (AD – BC) / 2;

AH = KD = (12 – 8) / 2 = 4/2 = 2 cm.

Behind the Pythagorean theorem:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 10 ^ 2 – 2 ^ 2 = 100 – 4 = 96;

BH = √96 ≈ 9.8 cm.

The area of the trapezoid is:

S = (12 + 8) / 2 * 9.8 = 20/2 * 9.8 = 10 * 9.8 = 98 cm2.

Answer: the area of the trapezoid is 98 cm2.