In trapezoid ABCD, the base of BC is equal to AB and 2 times less than AD.

| September 29, 2021 | education

In trapezoid ABCD, the base of BC is equal to AB and 2 times less than AD. Find the area of the trapezoid given that AC = 12, CD = 15.

On a larger base AD, mark the point H – the middle of AD, then AH = DH = AB = AB, and therefore the quadrilateral ABCH is a rhombus.

The BCН triangle is isosceles, BC = СН, the СНD triangle is so de isosceles, DH = СН, the angle СНD = ВСН as criss-crossing angles. Then the BCH triangle is equal to the CDH triangle on two sides and the angle between them. Then BH = CD = 15 cm.

Let us determine the area of ​​the rhombus ABCН.

S1 = AC * ВН / 2 = 12 * 15/2 = 90 cm2.

Since the diagonal of the rhombus divides it into two equal triangles, then Svsn = Ssdn = S1 / 2 = 45 cm2.

Then the area of ​​the trapezoid is equal to: Savsd = S1 + Ssdn = 90 + 45 = 135 cm2.

Answer: The area of ​​the trapezoid is 135 cm2.



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