Lateral sides 20 and 34, bases 18 and 60. Find the area of the trapezoid.

Let’s build the heights of the trapezoid BH and CK. Quadrangle НВСК is a rectangle, then НК = 18 cm.

Let the length of the segment AH = X cm, then DK = (AD – HK – AH) = (60 – 18 – X) = (42 – X).

In right-angled triangles ABН and CDK, we express the heights of BH and СK.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 400 – X ^ 2.

CK ^ 2 = CD ^ 2 – DK ^ 2 = 1156 – 1764 + 84 * X – X ^ 2.

Since BH = CK, then:

400 – X ^ 2 = 1156 – 1764 + 84 * X – X ^ 2.

84 * X = 1008.

X = AH = 1008/84 = 12 cm.

Then BH ^ 2 = 400 – 144 = 256.

BH = 16 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (18 + 60) * 16/2 = 624 cm2.

Answer: The area of the trapezoid is 624 cm2.