The upper base of an isosceles trapezoid is 10, the lower base is 52. The sides of the trapezoid are 29.

The upper base of an isosceles trapezoid is 10, the lower base is 52. The sides of the trapezoid are 29. Find the area of the trapezoid.

Isosceles is a trapezoid in which the sides are equal.

The area of ​​a trapezoid is the product of the half-sum of its bases and the height:

S = (a + b) / 2 h, where:

S is the area of ​​the trapezoid;

a – smaller base;

b – larger base;

h is the height of the trapezoid.

Let’s draw two heights BH and CK.

Since the segment of the larger base located between two heights is equal to the length of the larger base, then:

NK = BC;

AH = KD = (AD – BC) / 2;

AH = KD = (52 – 10) / 2 = 42/2 = 21 cm.

To calculate the height BH, consider the triangle ΔABH.

Let’s apply the Pythagorean theorem:

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

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 29 ^ 2 – 21 ^ 2 = 841 – 441 = 400;

BH = √400 = 20 cm.

S = (52 + 10) / 2 20 = 62/2 20 = 31 20 = 620 cm2.

Answer: the area of ​​the trapezoid is 620 cm2.