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

| September 19, 2021 | education

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

By condition, AB = CD, which means the trapezoid is isosceles.

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

AH = (AB + AD) / 2.

The middle line of the trapezoid is also equal to the half-sum of the bases of the trapezoid.

KM = (AB + AD) / 2.

AH = KM = 7 cm

Consider a right-angled triangle ACN, in which AH = KM = 7 cm, and tgA = 0.6, since

tgA = CH / AN.

0.6 = CH / 7.

CH = 7 * 0.6 = 4.2 cm.

Then the area of the trapezoid will be S = CH * KM = 4.2 * 7 = 29.4 cm2.

Answer: S = 29.4 cm2.



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