The larger base of an isosceles trapezoid is 22m, the side is 8.5m and the diagonal is 19.5m.

| June 16, 2021 | education

The larger base of an isosceles trapezoid is 22m, the side is 8.5m and the diagonal is 19.5m. Determine the area of the trapezoid.

In a triangle ACD, the lengths of all its sides are known, we determine its area by Heron’s theorem.

Let us define the semiperimeter of the triangle. p = (22 + 8.5 + 19.5) = 25 m.

Then Sacd = √25 * (25 – 22) * (25 – 19.5) * (25 – 8.5) = √25 * 3 * 5.5 * 16.5 = √6806.25 = 82.5 m2 …

The area of ​​the triangle ACD is thus equal to Sacd = AD * CH / 2, then CH = 2 * S / AD = 2 * 82.5 / 22 = 7.5 m.

In a right-angled triangle CDH DH ^ 2 = CD ^ 2 – CH ^ 2 = 8.5 ^ 2 – 7.5 ^ 2 = 72.25 – 56.25 = 16.

DН = 4 m.

Since the trapezoid is isosceles, the length DH is equal to the half-difference of the lengths of the bases of the trapezoid.

DH = (AD – BC) / 2, then BC = AD – 2 * DH = 22 – 2 * 4 = 14 m.

Determine the area of ​​the trapezoid. Savsd = (ВС + АD) * СН / 2 = (14 + 22) * 7.5 / 2 = 135 m2.

Answer: The area of ​​the trapezoid is 135 m2.



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