In an isosceles trapezoid, the base is 51 cm and 69 cm. The angle at the base is 45 degrees.

In an isosceles trapezoid, the base is 51 cm and 69 cm. The angle at the base is 45 degrees. Find the area of the trapezoid.

Let’s draw the height of the CH trapezoid to its larger base. The CH height divides the larger base into two segments, the length of the smaller one being equal to the half difference of the base lengths.

DН = (АD – ВС) / 2 = (69 – 51) / 2 = 18/2 = 9 cm.

In a right-angled triangle CDH, one of the acute angles is 45, then the lengths of the legs in the triangle are equal.

DH = CH = 9 cm.

Determine the area of the trapezoid.

Savsd = (AD + BC) * CH / 2 = (69 + 51) * 9/2 = 18 * 9/2 = 540 cm2.

Answer: The area of the trapezoid is 540 cm2.