In the rectangular trapezoid ABCK, the large lateral side is equal to 3√2 cm, the angle K is 45 °, and the height CH

In the rectangular trapezoid ABCK, the large lateral side is equal to 3√2 cm, the angle K is 45 °, and the height CH divides the base of the AK in half. Find the area of the trapezoid.

Consider a right-angled triangle СНK, for which, by condition, the angle СKН = 45, then the angle НСK = 180 – СНK – СKН = 180 – 90 – 45 = 45.

Then the СKН triangle is rectangular and equilateral, CH = KН.

СН = СK * Sin45 = З * √2 * √2 / 2 = 3 cm.

KН = СK = 3 cm.

By condition, AH = KH = 3 cm, then AK = AH + KH = 3 + 3 = 6 cm.

Quadrangle ABCН is a rectangle, then BC = AH = 3 cm.

Determine the area of the trapezoid ABSK.

Savsk = (BC + AK) * CH / 2 = (3 + 6) * 3/2 = 13.5 cm2.

Answer: The area of the trapezoid is 13.5 cm2.