The heights drawn from the vertices of the smaller base of an isosceles trapezoid divide the larger base into three segments

The heights drawn from the vertices of the smaller base of an isosceles trapezoid divide the larger base into three segments, the sum of two of which is equal to the third. Find the area of this trapezoid if its smaller base and height are 6 cm each.

Since BН and СР are the heights of the trapezoid, then the quadrilateral HBСР is a rectangle, then НР = ВС = 6 cm.

By condition, (AН + DP) = HP = 6 cm, then AD = (AН + DP) + HP = 6 + 6 = 12 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * BH / 2 = (6 + 12) * 6/2 = 54 cm2.

Answer: The area of the trapezoid is 54 cm2.