In a trapezoid, the lengths of the bases are 4 and 11, and the lengths of the diagonals are 14 and 13.

| February 1, 2021 | education

In a trapezoid, the lengths of the bases are 4 and 11, and the lengths of the diagonals are 14 and 13. Find the height and area of the trapezoid.

Draw a straight line СК parallel to the ВD diagonal through the vertex C of the trapezoid.

The quadrangle of the ВСKD is a parallelogram, then DK = ВС= 4 cm, СK = ВD = 14 cm.

The length of the segment AK = AD + DK = 11 + 4 = 15 cm.

The area of ​​the triangle AСK is determined by Heron’s theorem.

Rask = (AС + СK + AK) / 2 = (13 + 14 + 15) / 2 = 42/2 = 21 cm.

Sask = √p * (p – AC) * (p – CК) * (p – AK) = √21 * 8 * 7 * 6 = √7056 = 84 cm2.

The length of the base of the AK is equal to the sum of the lengths of the bases of the trapezium, the height of the НM is total, then Savsd = Sask = 84 cm2.

Savsd = (BC + BP) * НM / 2.

НM = 2 * Savsd / (ВС + AD) = 2 * 84/15 = 56/5 = 11 (1/5) cm.

Answer: The area of ​​the trapezoid is 84 cm2, the height is 11 (1/5) cm.



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