Question

Основания трапеции равны 3см и 2 см.Диагонали её равны 4 см и 3 см.Найдите площадь трапеции

Answer 1

Будет 14 сантиметров

Answer 2

Given Information:

We are given that the bases of the trapezoid are 3 cm and 2 cm, and the diagonals are 4 cm and 3 cm.

Formula for the Area of a Trapezoid:

The formula for the area of a trapezoid is A = (a + b) * h / 2, where A is the area, a and b are the lengths of the bases, and h is the height.

Finding the Height of the Trapezoid:

To find the height of the trapezoid, we can use the Pythagorean theorem. The diagonals of a trapezoid divide it into four right triangles. The height of the trapezoid is the length of the perpendicular line segment connecting the two bases.

Using the Pythagorean theorem, we have h^2 = d^2 - ((b - a) / 2)^2, where h is the height and d is the difference between the lengths of the diagonals.

Substituting the given values, we have h^2 = 4^2 - ((3 - 2) / 2)^2.

Calculating the values, we get h^2 = 16 - (1 / 2)^2 = 16 - 1 / 4 = 15.75.

Taking the square root of both sides, we get h = √15.75 ≈ 3.97 cm.

Calculating the Area of the Trapezoid:

Now that we have the height of the trapezoid, we can substitute the values into the formula for the area of a trapezoid.

Using the formula A = (a + b) * h / 2, where a = 3 cm, b = 2 cm, and h ≈ 3.97 cm, we can calculate the area.

Substituting the values, we have A = (3 + 2) * 3.97 / 2.

Calculating the values, we get A = 5 * 3.97 / 2 ≈ 9.925 cm^2.

Answer:

The area of the trapezoid is approximately 9.925 cm^2.