The area of a rectangular trapezoid is 120 square cm, and its height is 8 cm.Find all sides of the trapezoid

| May 4, 2021 | education

The area of a rectangular trapezoid is 120 square cm, and its height is 8 cm.Find all sides of the trapezoid if one of the bases is 6 cm larger than the other.

Let the area of ​​a rectangular trapezoid ABCD with bases AD and BC be S = 120 cm ^ 2, ∠BAD = 90 °, its height AB = 8 cm.Since it is known from the condition of the problem that one of the bases is 6 cm larger than the other, then BC = x cm, and AD = x + 6 cm.
From the vertex C we draw the height CE = AB = 8 cm, in the resulting square ABCE, the sides AE = BC, then the segment ED = AD – AE = AD – BC = (x + 6) – x = 6 (cm). Consider a rectangular Δ CED (∠CED = 90 °), in which we find the side of CD according to the Pythagorean theorem: CD ^ 2 = CE ^ 2 + ED ^ 2; CD ^ 2 = (8 cm) ^ 2 + (6 cm) ^ 2; CD ^ 2 = 100 cm ^ 2, then CD = 10 cm.
The area of ​​the trapezoid can be found by the formula S = AB ∙ (BC + AD): 2, on the other hand S = 120 cm ^ 2, we get the equation: 8 ∙ ((x + 6) + x): 2 = 120; x = 12 cm; BC = 12 cm; AD = 12 + 6; AD = 18 cm.
Answer: the side of the trapezoid is 10 cm, the bases are 12 cm and 18 cm.



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