Question

периметр прямоугольной трапеции описанной около окружности равен 80 а большая из боковых сторон равна 24 найдите радиус окружности

Answer 1

сумма оснований трапеции= сумме боковых сторон( то есть по 40)

а+с=в+d

 

отсюда

а=(в+d)-с=40-24=16 малая боковая сторона

r=16|2=8

 

Answer 2

Finding the Radius of the Circumscribed Circle of a Trapezoid

To find the radius of the circumscribed circle of a trapezoid, we can use the formula for the perimeter of a trapezoid and the given information about the trapezoid.

The perimeter of a trapezoid can be calculated using the formula: Perimeter = sum of all sides

Given: - Perimeter of the trapezoid = 80 - Length of the larger of the two parallel sides = 24

Using the given information, we can calculate the length of the other parallel side and then proceed to find the radius of the circumscribed circle.

Calculation Steps:

1. Calculate the length of the other parallel side of the trapezoid. 2. Use the trapezoid's sides to find the radius of the circumscribed circle.

Calculation:

1. Calculating the Length of the Other Parallel Side: - Let's denote the lengths of the two parallel sides as a and b. - Given that the larger of the two parallel sides is 24, we can denote it as a = 24. - Using the formula for the perimeter of a trapezoid, we can express the sum of all sides as: Perimeter = a + b + 2 * (length of non-parallel sides) - Given that the perimeter of the trapezoid is 80, we can express this as: 80 = 24 + b + 2 * (length of non-parallel sides) - Solving for b, we get: b = 80 - 24 - 2 * (length of non-parallel sides)

2. Finding the Radius of the Circumscribed Circle: - Once we have the lengths of the two parallel sides, we can use these lengths to find the radius of the circumscribed circle using the formula: Radius of circumscribed circle = (a * b * c) / (4 * Area of the trapezoid) - The area of a trapezoid can be calculated using the formula: Area = (1/2) * (sum of parallel sides) * (distance between them) - After finding the area, we can use it to calculate the radius of the circumscribed circle.

Conclusion:

By following these steps, we can calculate the length of the other parallel side of the trapezoid and then use the lengths of the parallel sides to find the radius of the circumscribed circle.