# The bases of an isosceles trapezoid are 1 and 33, and its area is 204. Find the perimeter of the trapezoid.

1. Vertices of a trapezoid A, B, C, D. BC = 1 unit of measurement. AD = 33 units.

BК – height.

2. Calculate the length BK. For the calculation, we use the formula for the area of ​​a trapezoid:

(AD + BC) / 2 x ВK = 204.

BK = 204 x 2 / (AD + BC) = 408 / (33 + 1) = 12 units.

3. Calculate the length of the segment AK:

AK = (AD – BC) / 2 = (33 – 1) / 2 = 16 units.

4. Calculate the length of the side AB. In a right-angled triangle ABK, it is

hypotenuse. The calculation is made using the Pythagorean theorem:

AB = √AK² + BK² = √16² + 12² = √256 + 144 = √400 = 20 units.

5. СD = AB = 20 units of measurement.

6. Calculate the perimeter (P) of a given geometric figure:

P = 20 + 20 + 1 + 33 = 74 units.

Answer: The perimeter of a trapezoid is 74 units. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.