Question

В равнобедренной трапеции диагональ равна 25 см,а высота 15 см.Найти площадь трапеции.

Answer 1

В равнобедренном треугольнике, высота, проведенная из вершины на большее основание, делит его на два отрезка, один из которых равен полусумме оснований (т.е. ср. линии), а другой полуразности оснований. По т. Пифагора АК=√(625-225)=√400=20. Значит средняя линия равна 20. S=20*15=300

Answer 2

25^2=х^2+15^2=<х=20
Площадь равна произведению полусуммы оснований на высоту и равна S=15*20=300

Answer 3

Finding the Area of a Trapezoid

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

Area = (1/2) * (sum of the bases) * height

In this case, we are given that the height of the trapezoid is 15 cm and the diagonal is 25 cm. However, we need to find the lengths of the bases in order to calculate the area.

Let's denote the lengths of the bases as a and b. We can use the Pythagorean theorem to find the lengths of the bases.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

Let's consider the trapezoid as a right triangle by drawing a perpendicular from one of the bases to the diagonal. This will create two right triangles.

Using the Pythagorean theorem, we can write the following equations:

a^2 + h^2 = d^2 (Equation 1)

b^2 + h^2 = d^2 (Equation 2)

where: - a is the length of one base - b is the length of the other base - h is the height of the trapezoid - d is the length of the diagonal

Since both Equation 1 and Equation 2 are equal to d^2, we can equate them:

a^2 + h^2 = b^2 + h^2

Simplifying the equation, we get:

a^2 = b^2

This means that the lengths of the bases are equal in a trapezoid. Therefore, we can denote the length of both bases as a.

Now, we can substitute the values into the formula to find the area:

Area = (1/2) * (a + a) * h = a * h

Substituting the given values, we have:

Area = 15 cm * a

To find the value of a, we can use the Pythagorean theorem again. Since the diagonal is 25 cm and the height is 15 cm, we can write:

a^2 + 15^2 = 25^2

Simplifying the equation, we get:

a^2 + 225 = 625

a^2 = 400

Taking the square root of both sides, we find:

a = 20 cm

Now, we can substitute the value of a into the formula to find the area:

Area = 15 cm * 20 cm = 300 cm^2

Therefore, the area of the trapezoid is 300 cm^2.

Answer

The area of the trapezoid is 300 cm^2.