Question

Найдите площадь трапеции, вершины которой имеют координаты (1;1) (10;1) (7;8) (8;2)Помогите... Пожалуйста!!!

Answer 1

По Вашим координатам не получается трапеция (см.рис.). Проверьте условия.

Answer 2

Calculation of Trapezoid Area

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

Area = (base1 + base2) * height / 2

Given the coordinates of the vertices of the trapezoid as (1,1), (10,1), (7,8), and (8,2), we can calculate the length of the bases and the height of the trapezoid.

Let's calculate the length of the bases first:

- The length of the base1 is the distance between the points (1,1) and (10,1). - The length of the base2 is the distance between the points (7,8) and (8,2).

Using the distance formula, the length of the base1 is:

base1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we get:

base1 = sqrt((10 - 1)^2 + (1 - 1)^2) = sqrt(9^2 + 0^2) = sqrt(81) = 9

Similarly, the length of the base2 is:

base2 = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we get:

base2 = sqrt((8 - 7)^2 + (2 - 8)^2) = sqrt(1^2 + (-6)^2) = sqrt(1 + 36) = sqrt(37)

Next, let's calculate the height of the trapezoid:

- The height of the trapezoid is the vertical distance between the bases.

To find the height, we can consider the difference in the y-coordinates of the points (7,8) and (1,1):

height = y2 - y1 = 8 - 1 = 7

Now that we have the values for base1, base2, and height, we can calculate the area of the trapezoid using the formula:

Area = (base1 + base2) * height / 2

Substituting the values, we get:

Area = (9 + sqrt(37)) * 7 / 2

Calculating the value, we find:

Area ≈ 31.5 square units

Therefore, the area of the trapezoid with vertices (1,1), (10,1), (7,8), and (8,2) is approximately 31.5 square units.

Please let me know if there is anything else I can help you with!