Find the angles of the trapezoid BC = 15 cm, AD = 49 cm. Find the perimeter ABCD.

BC = 15 cm, AD = 49 cm, angle A = angle D = 60 °.

Since this is an isosceles trapezoid, then:

P = AB + BC + CD + AD = 2AB + BC + AD.

We find AB as follows: draw two heights from points B and C and get points K and T (AK = TD) and a triangle ABK, from which we recognize the side AB:

cos 60 ° = AK / AB,

AB = AK / cos 60 °,

where AK = (AD – BC) / 2 = (49 – 15) / 2 = 34/2 = 17 cm,

AB = 17 / cos 60 ° = 17: 1/2 = 34 cm.

Let’s find the perimeter by the formula:

P = 2AB + BC + AD = 2 * 34 + 15 + 49 = 132 cm.

Answer: the perimeter is 132 cm.