The trapezoid bases are 5 and 40, one of the sides is 14, and the cosine of the angle between it and one of the bases is 3/5. Find the area of the trapezoid
The area of the trapezoid is equal to the product of half the sum of the bases in height. The grounds are known to us, we will find the height.
By definition, cos (/ CDE) = ED / CD
3/5 = ED / 14
ED = 3 * 14/5 = 8.4
By the Pythagorean theorem:
CD ^ 2 = ED ^ 2 + EC ^ 2
14 ^ 2 = 8.4 ^ 2 + EC ^ 2
196 = 70.56 + EC ^ 2
EC ^ 2 = 125.44
EC = 11.2 – this is the height
S trapezoid = EC * (BC + AD) / 2
S trapezoid = 11.2 * (5 + 40) / 2
S trapezoid = 5.6 * 45 = 252
Answer: S trapezoid = 252
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