In trapezoid ABCD, the base of BC is 1 cm, the lateral side of AB is inclined with the base of AD at an angle of 45 degrees
| August 15, 2021 | education
In trapezoid ABCD, the base of BC is 1 cm, the lateral side of AB is inclined with the base of AD at an angle of 45 degrees. Point F – the base of the trapezoid height – divides the AD side into segments AF = 6 cm and FD = 11 cm. Find the area of the trapezoid.
Since BF is the height of a trapezoid, triangle ABF is rectangular.
The angle BAD, by condition, is equal to 45, then the triangle ABF is rectangular and isosceles, BF = AF = 6 cm.
Determine the length of the larger base.
AD = AF + DF = 6 + 11 = 17 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * BF / 2 = (1 + 17) * 6/2 = 18 * 6/2 = 54 cm2.
Answer: The area of the trapezoid is 54 cm2
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