# The smaller base of the isosceles trapezoid is equal to the lateral side. height = 8cm, perimeter = 52cm

**The smaller base of the isosceles trapezoid is equal to the lateral side. height = 8cm, perimeter = 52cm, and area = 128cm squared. find the lengths of the sides of the trapezoid**

1. Vertices of the trapezoid – A, B, C, D. AB = BC = CD. BE – height. S is the area of the trapezoid.

P is the perimeter.

2. Calculate the length of the base AD, using the formula for calculating the area of the trapezoid:

S = AD x BE = 128 centimeters².

AD = S: BE = 128: 8 = 16 centimeters.

3. We calculate the length of the side AB, using the formula for calculating the perimeter of the trapezoid and taking into account that AB = BC = CD:

P = 3AB + AD = 52 centimeters.

3AB = 52 – 16 = 36 centimeters.

AB = 12 centimeters.

Answer: AB = BC = CD = 12 centimeters. AD = 16 centimeters.