The bases of the trapezoid are 7 and 8 and the diagonals are 9 and 12. Find the height of the trapezoid.

univerkov | August 7, 2021 | education

Through vertex C, construct a segment CK parallel to BD. The quadrangle ВСКD is a parallelogram, then DК = ВС = 7 cm, СK = ВD = 9 cm.

The length of the segment AK = AD + DK = AD + BC = 8 + 7 = 15 cm

By Heron’s theorem, we define the area of the triangle ACK.

The semi-perimeter of the ACK triangle is: p = (12 + 9 + 15) / 2 = 18 cm.

Then Sask = √18 * (18 – 12) * (18 – 9) * (18 – 15) = √2916 = 54 cm2.

Then Savsd = 54 cm2.

Answer: The area of the trapezoid is 54 cm2.

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