From the top B of the trapezoid ABCD, we will construct the height BH. Since the trapezoid ABCD is isosceles, the height BH divides the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the bases.
AH = (AD – BC) / 2 = (24 – 10) / 2 = 7 cm.
In a right-angled triangle ABH, the angle ABH = ABC – CBH = 135 – 90 = 45.
Then the triangle ABH is isosceles, BH = AH = 7 cm.
Determine the area of the trapezoid. Savsd = (ВС + АD) * ВН = (10 + 24) * 7/2 = 119 cm2.
Answer: The area of the trapezoid is 119 cm2.
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