Question

Знайдіть площу чотирикутника,вершини якого є серединами сторін ромба з діагоналями завдожки 14 см і 20 см

Answer 1

По теореме Вариньона: Середины сторон ромба являются вершинами параллелограмма

Answer 2

Finding the Area of a Quadrilateral

To find the area of a quadrilateral with vertices as the midpoints of the sides of a rhombus with diagonals of length 14 cm and 20 cm, we can use the formula for the area of a quadrilateral when the coordinates of its vertices are known.

The formula for the area of a quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) is given by:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) + x4(y2 - y1)|

Let's calculate the area using the given information.

Calculation

Given: - Diagonal 1 (d1) = 14 cm - Diagonal 2 (d2) = 20 cm

We know that the diagonals of a rhombus intersect at right angles and bisect each other. The formula for the length of the sides of a rhombus in terms of its diagonals is given by: Side = sqrt((d1/2)^2 + (d2/2)^2)

Substituting the given values: Side = sqrt((14/2)^2 + (20/2)^2) Side = sqrt(49 + 100) Side = sqrt(149) cm

Now, we can use the coordinates of the midpoints of the sides of the rhombus to calculate the area of the quadrilateral.

Conclusion

The area of the quadrilateral with vertices as the midpoints of the sides of the rhombus with diagonals of length 14 cm and 20 cm is calculated to be sqrt(149) square centimeters.