Question

Прямоугольная трапеция с бедрами - 3 см и 5 см . Периметр трапеции- 20 см, площадь неизвестна. Найдите площадь

Answer 1

В прямоугольной трапеции одна из боковых сторон перпендикулярна основаниям, причём эта сторона будет иметь наименьшую длину  ( т.к. кратчайшее расстояние - это длина перпендикуляра ). Эта же сторона будет являться высотой трапеции. Итак, высота трапеции = 3 см.
Сумма оснований трапеции равна  20-(3+5)=20-8=12 (см).
Площадь трапеции = полусумме оснований трапеции, умноженной на высоту трапеции:
  S=(12:2)*3=6*3=18 (cм²)

Answer 2

Calculating the Area of a Trapezoid

To find the area of a trapezoid, we can use the formula:

Area = (1/2) * (sum of the lengths of the parallel sides) * (height)

In this case, the trapezoid has parallel sides of 3 cm and 5 cm, and the perimeter is 20 cm. We can use this information to find the height and then calculate the area.

Calculating the Height of the Trapezoid

First, let's calculate the height of the trapezoid using the given perimeter and the lengths of the parallel sides.

The perimeter of a trapezoid can be calculated using the formula:

Perimeter = sum of all sides

Given that the perimeter is 20 cm and the parallel sides are 3 cm and 5 cm, we can calculate the length of the non-parallel sides.

The non-parallel sides can be calculated as follows: - Let the length of the non-parallel side be x. - The sum of all sides is 20 cm, so the non-parallel sides add up to 20 - (3 + 5) = 20 - 8 = 12 cm. - Since the non-parallel sides are of equal length, each non-parallel side is 12 / 2 = 6 cm.

Now that we have the lengths of the non-parallel sides, we can use them to calculate the height of the trapezoid.

The height can be calculated using the formula: height = √(side1^2 - side2^2)

Where side1 and side2 are the non-parallel sides.

Calculating the Area of the Trapezoid

Now that we have the height, we can use the formula for the area of a trapezoid to find the area.

Area = (1/2) * (sum of the lengths of the parallel sides) * (height)

Let's calculate the height and then use it to find the area of the trapezoid.