In an isosceles trapezoid ABCD, the side length is 10 cm, less than 4 cm, and the height is 6 cm.

In an isosceles trapezoid ABCD, the side length is 10 cm, less than 4 cm, and the height is 6 cm. Find the area of the trapezoid.

Since the area of ​​the trapezoid is equal to the product of the half-sum of its bases by the height:

S = (ВС + АD) / 2 h, then:

it is necessary to calculate the length of the greater base AD.

Since the smaller base of the BC is equal to the length of the НK segment, which is located between the heights of the ВН and СK, then:

AD = BC + AH + KD.

Since this trapezoid is isosceles, the segments AH and KD are equal to each other. To calculate their length, consider the triangle ΔАВН. This triangle is right-angled, so we apply the Pythagorean theorem:

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

AH ^ 2 = AB ^ 2 – BH ^ 2;

AH ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

AH ^ 2 = √64 = 8 cm.

AD = 4 + 8 + 8 = 20 cm.

S = (20 + 4) / 2 * 6 = 24/2 * 6 = 12 6 = 72 cm2.

Answer: the area of ​​the trapezoid is 72 cm2.