The diagonal of an isosceles trapezoid divides its acute angle in half.

The diagonal of an isosceles trapezoid divides its acute angle in half. The bases of the trapezoid are 6 cm and 15 cm. Find the perimeter of the trapezoid.

Since, by condition, the diagonal AC divides the angle BAD in half, the angle BAC = CAD.

Angle BCA = CAD as criss-crossing angles at the intersection of parallel straight lines AD and BC secant AC.

Then the angle BAC = BCA, and therefore the triangle ABC is isosceles, AB = BC.

Then AB = BC = CD = 6 cm.

Determine the perimeter of the trapezoid.

P = AB + BC + CD + AD = 6 + 6 + 6 + 15 = 33 cm.

Answer: The perimeter of the trapezoid is 33 cm.