Question

Основания трапеции равны 2см и 18 см а диагонали - 15 см и 7 см. Найдите площадь трапеции

Answer 1

В трапеции АВСД

Основания ВС=2и АД=18

Диагонали АС=7и ВД=15

опустим высоты ВN и СM

1)треугольники АСM = NBD

прямоугольные, где ВN = СM

ВС=NM=2

AN=x

AM=AN+NM=x+2

ND=AD- AN=18-x

2)По теореме Пифагора

СM ²=АС ²-АM² =49-х ²-4х-4

3)ВN ²=ВД ²–ND²=225-324+36х-х²

49-х² -4х-4=225-324+36х-х²

-4x+45=-99+36x

-40х=-144

х=3,6=АN

АM=3,6+2=5,6

4) СM ²=АС²-АM²

отсюда СM=√(49-31,36)=4,2

5)площадь АВСД=1/2*(ВС+АД)*СM=1/2(2+18)*4,2=42

Answer 2

Given Information:

We are given that the bases of the trapezoid are 2 cm and 18 cm, and the diagonals are 15 cm and 7 cm.

Finding the Height of the Trapezoid:

To find the height of the trapezoid, we can use the formula for the area of a trapezoid, which is given by:

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

We can rearrange this formula to solve for the height:

Height = (2 * Area) / (sum of the bases)

Finding the Area of the Trapezoid:

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

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

Substituting the given values, we have:

Area = (1/2) * (2 cm + 18 cm) * (height)

Calculation:

Let's calculate the height of the trapezoid first using the formula mentioned above.

Height = (2 * Area) / (sum of the bases)

Using the given values, we have:

Height = (2 * Area) / (2 cm + 18 cm)

Height = (2 * Area) / 20 cm

Now, let's calculate the area of the trapezoid using the formula mentioned above.

Area = (1/2) * (2 cm + 18 cm) * (height)

Substituting the value of the height we calculated earlier, we have:

Area = (1/2) * (2 cm + 18 cm) * [(2 * Area) / 20 cm]

Simplifying the equation, we get:

Area = (1/2) * (20 cm) * [(2 * Area) / 20 cm]

Area = (1/2) * 2 * Area

Area = Area

Since the area of the trapezoid is equal to itself, we cannot determine the exact value of the area without additional information.

Please provide any additional information or clarify the problem if necessary.