Question

Дано ABCD ромб диагонали равны 10 и 12 см найдите площадь и периметр. Помогите пожалуйста

Answer 1

S = 1/2*d1*d2 = 60

по теореме Пифагора одна сторона = √(25 + 36) = √61

тогда P = 4*√61

Answer 2

Finding the Area and Perimeter of a Rhombus

To find the area and perimeter of a rhombus, we need to know the lengths of its diagonals. In this case, the diagonals of the rhombus are given as 10 cm and 12 cm.

Step 1: Finding the Area

The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

In this case, the lengths of the diagonals are 10 cm and 12 cm. Plugging these values into the formula, we get:

Area = (10 cm * 12 cm) / 2 = 120 cm²

Therefore, the area of the rhombus is 120 cm².

Step 2: Finding the Perimeter

The perimeter of a rhombus can be calculated by multiplying the length of one side by 4. Since all sides of a rhombus are equal, we can choose any side length to calculate the perimeter.

To find the side length, we can use the Pythagorean theorem. The diagonals of a rhombus bisect each other at right angles, forming four congruent right triangles. The side length of the rhombus can be found using the Pythagorean theorem in one of these triangles.

Let's denote the side length as s. Using the Pythagorean theorem, we have:

s² = (d1/2)² + (d2/2)²

Substituting the given values, we get:

s² = (10 cm/2)² + (12 cm/2)² s² = 5 cm² + 6 cm² s² = 11 cm² s ≈ √11 cm

Now that we have the side length, we can calculate the perimeter:

Perimeter = 4 * s ≈ 4 * √11 cm

Therefore, the perimeter of the rhombus is approximately 4√11 cm.

To summarize: - The area of the rhombus is 120 cm². - The perimeter of the rhombus is approximately 4√11 cm.

Please note that the calculations provided are based on the given information and assumptions about the shape of the rhombus. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.