The bases of an isosceles trapezoid are 5.1 and 6.9 dm, the lateral side is 41 cm. Find its area.

| August 8, 2021 | education

Let’s convert the lengths of the bases to centimeters.

BC = 51 cm, AD = 69 cm.

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-sum of the bases.

DН = (АD – ВС) / 2 = (69 – 51) / 2 = 18/2 = 9 cm.

AH = (AD + BC) / 2 = (69 + 51) / 2 = 120/2 = 60 cm.

From the right-angled triangle CHD, by the Pythagorean theorem, we define the leg CH, which is the height of the trapezoid.

CH ^ 2 = CD ^ 2 – DH ^ 2 = 412 – 92 = 1681 – 81 = 1600.

CH = √1600 = 40 cm.

Determine the area of ​​the trapezoid.

S = (AD + BC) * CH / 2 = (69 + 51) * 40/2 = 2400 cm2.

Answer: The area of ​​the trapezoid is 2400 cm2.



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