Question

В равнобедренной трапеции основания равны 8 см и 16 см, а угол при основании равен 45 градусов. Чему равна площадь трапеции?

Answer 1

Найдем площадь трапеции через высоту. Для этого сначала узнаем эту высоту по формуле :h=sin a = a-b/2 * tg a ... где а - большая сторона.
получится 4 см...
и теперь площадь по формуле : S=1/2 (a-b) * h
будет равно 1/2 * 8 * 4 = 16 кв.см.

Answer 2

Calculation of the Trapezoid's Area

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

Area = (a + b) * h / 2

where: - a and b are the lengths of the bases of the trapezoid - h is the height of the trapezoid, which is the perpendicular distance between the bases

In this case, the trapezoid is isosceles, meaning that the lengths of the bases are equal. Given that the lengths of the bases are 8 cm and 16 cm, we can calculate the area.

Let's substitute the values into the formula:

Area = (8 + 16) * h / 2

Now, we need to find the height of the trapezoid. To do that, we can use the given information that the angle at the base is 45 degrees.

From the search results, we can see that the sum of the angles in a trapezoid is 360 degrees Since the trapezoid is isosceles, the opposite angles are equal. Therefore, the angle at the top of the trapezoid is also 45 degrees.

Using trigonometry, we can find the height of the trapezoid. Let's consider the right triangle formed by the height, the base, and the angle at the base. The opposite side of the angle is the height, and the adjacent side is half of the difference between the lengths of the bases.

From the search results, we can see that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side Therefore, we can write:

tan(45) = h / ((16 - 8) / 2)

Simplifying the equation:

1 = h / 4

h = 4

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

Area = (8 + 16) * 4 / 2

Area = 24 * 4 / 2

Area = 48 square cm

Therefore, the area of the trapezoid is 48 square cm.

Conclusion

The area of the given trapezoid with bases measuring 8 cm and 16 cm, and an angle of 45 degrees at the base, is 48 square cm.