In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the greater base of AD.

| May 18, 2021 | education

In trapezoid ABCD, the sides AB and CD are equal, CH is the height drawn to the greater base of AD. Find the area of this trapezoid if tg∠CAH = 0.6 and the middle line of the trapezoid is 7.

Let us use the property of the height of an isosceles trapezoid drawn from the top of a smaller base.

The height of an isosceles trapezoid divides the larger base into two segments, the larger of which is equal to the half-sum of the lengths of the bases, and the smaller half-difference.

AH = (AD + BC) / 2.

DH = (AD – BC) / 2.

Then the segment AH is equal to the midline of the trapezoid. AH = KM = 7 cm.

From a right-angled triangle, we determine the height of the CH.

CH = AN * tgsan = 7 * 0.6 = 4.2 cm.

The area of the trapezoid is equal to: Savsd = (BC + AD) * CH / 2 = KM * CH = 7 * 4.2 = 29.4 cm2.

Answer: The area of the trapezoid is 29.4 cm2.



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