In isosceles trapezoid ABCD, angle A = 60 degrees, side length AB is 10 cm, BC = 4 cm.

| July 9, 2021 | education

In isosceles trapezoid ABCD, angle A = 60 degrees, side length AB is 10 cm, BC = 4 cm. Calculate the perimeter of triangle ABCD.

Let us draw two heights BH and K from the vertices of the obtuse angles of the trapezoid.

In a right-angled triangle ABН, we determine the length of the leg AH.

Sin60 = AH / AB.

AH = AB * Cos60 = 10 * 1/2 = 5 cm.

Since the trapezoid is isosceles, the angle BАН = СDК, and the segment AB = СD, then the right-angled triangles ABH and СDK are equal in hypotenuse and acute angles, which means AH = DC = 5 cm.

Quadrilateral BCDK rectangle, then НC = BC = 4 cm.

Base length АD = АН + НК + DК = 5 + 4 + 5 = 14 cm.

Let’s define the perimeter of the trapezoid. P = AB + BC + CD + AD = 10 + 4 + 10 + 14 = 38 cm.

Answer: The area of the trapezoid is 38 cm.



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