The base of the trapezoid is 37 cm and the middle line is 25 cm. Find the second base of the trapezoid

| June 17, 2021 | education

The base of the trapezoid is 37 cm and the middle line is 25 cm. Find the second base of the trapezoid 398. The area of the trapezoid is 100 m2, its height is 8 m. Find the base of the trapezoid if their difference is 7 m.

Since the middle line of a trapezoid is equal to the half-sum of its bases: m = (a + b) / 2 and it is known that m = 25; b = 37, we find the value of the base a: a = 2 * m – b = 2 * 25 – 37 = 50 – 37 = 13.

The area of the trapezoid is: S = (a + b) / 2 * h. Since we know the height of the trapezoid and its area, we can express the sum of the bases: a + b = S * 2 / h = 200/8 = 25. Now we can express the value of a from this equation: a = 25 – b. Since we know that the base difference is 7, then: a – b = 7; 25 – b – b = 7; 2 * b = 18; b = 9. Now find the value of a: a = 25 – b = 25 – 9 = 16.



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