Question

Периметр ромба равен 80 ,а один из углов 150. найдите площадь ромба

Answer 1

S = ½ a² sin150° S = ½ 20² ½ = 100 см² Ответ: 100 см²

Answer 2

Finding the Area of a Rhombus

To find the area of a rhombus, we can use the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals of the rhombus.

Given Information

- The perimeter of the rhombus is 80. - One of the angles of the rhombus is 150 degrees.

Solution

1. Finding the Length of Each Side - The perimeter of a rhombus is given by the formula: Perimeter = 4 * side length. - Given that the perimeter is 80, we can find the length of each side: side length = Perimeter / 4. - Substituting the given perimeter value: side length = 80 / 4 = 20.

2. Finding the Diagonals - The diagonals of a rhombus bisect each other at right angles, forming four right-angled triangles. - One of the angles in each of these triangles is 150 degrees, and the hypotenuse is the side length of the rhombus.

3. Using Trigonometry to Find the Diagonals - We can use trigonometric functions to find the length of the diagonals. - The formula to find the length of a side in a right-angled triangle is: side length = hypotenuse * sin(angle). - Substituting the given angle and side length: diagonal length = 20 * sin(150°).

4. Calculating the Diagonal Length - Using a calculator, we find: sin(150°) ≈ 0.5. - Therefore, the length of each diagonal is: diagonal length ≈ 20 * 0.5 = 10.

5. Finding the Area - Now that we have the lengths of the diagonals, we can use the formula for the area of a rhombus: Area = (d1 * d2) / 2. - Substituting the diagonal lengths: Area = (10 * 10) / 2 = 50.

Conclusion

The area of the given rhombus is approximately 50 square units.