The bases of an isosceles trapezoid are 7 and 19 and its area is 104. Find the side of the trapezoid.

| June 22, 2021 | education

Let us lower the height from the top of the obtuse angle C to the larger base AD.

By the property of an isosceles trapezoid, the height lowered from the apex of an obtuse angle to the larger base divides it into two segments, the smaller of which is equal to the half difference of the bases, and the larger half the sum of the bases.

DН = (АD – ВС) / 2 = (19 – 7) / 2 = 12/2 = 6 cm.

By condition, the area of ​​the trapezoid is 104 cm2.

104 = (AD + BC) * CH / 2.

104 = (19 + 7) * CH / 2.

CH = 2 * 104/26 = 8 cm.

From the right-angled triangle СНD, according to the Pythagorean theorem, we define the hypotenuse СD, which is the lateral side of the trapezoid.

CD ^ 2 = CH ^ 2 + DH ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 – 36 = 100.

СD = √100 = 10 cm.

Answer: The side of the trapezoid is 10 cm.



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