The bases of an isosceles trapezoid are 1 and 33, and its area is 204. Find the perimeter of the trapezoid.
July 24, 2021 | education
| 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.
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