In an isosceles trapezoid, the diagonal is the bisector of an acute angle, and the bases are equal to a and b.

In an isosceles trapezoid, the diagonal is the bisector of an acute angle, and the bases are equal to a and b. Find the perimeter of the trapezoid if a = 62 mm, b = 10 cm.

Since AC is a diagonal and a bisector, the angle BAC and CAD are equal to each other, and the angle BCA = CAD as criss-crossing angles at the intersection of parallel lines of the secant AC. Then the angle BAC = BAC, and therefore the triangle ABC is isosceles, AB = BC = 62 mm = 6.2 cm.

Since the trapezoid is isosceles, then CD = AB = BC = 6.2 cm.

Let’s define the perimeter of the trapezoid:

P = AB + BC + CD + AD = 6.2 + 6.2 + 6.2 + 10 = 28.6 cm.

Answer: The perimeter of the trapezoid is 28.6 cm.