Question

Диагонали рома равны 12 см и 16 см .Найдите площадь и периметр рома .

Answer 1

S= d1*d2\2=12*16\2=96
По теореме пифагора находим сторону ромба:
12^2+16^2=20^2
сторона = 20
Р=20*4=80

Answer 2

Calculation of 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 lengths of the diagonals are given as 12 cm and 16 cm.

Area of a Rhombus

The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2.

Substituting the given values, we have: Area = (12 cm * 16 cm) / 2 = 192 cm².

Therefore, the area of the rhombus is 192 cm².

Perimeter of a Rhombus

The perimeter of a rhombus can be calculated by multiplying the length of one side by 4. Since the sides of a rhombus are equal in length, we only need to find the length of one side.

To find the length of one side, we can use the Pythagorean theorem. The diagonals of a rhombus bisect each other at right angles, forming four congruent right triangles. The length of one side can be found using the formula: side = sqrt((diagonal1/2)^2 + (diagonal2/2)^2).

Substituting the given values, we have: side = sqrt((12 cm/2)^2 + (16 cm/2)^2) = sqrt(36 cm² + 64 cm²) = sqrt(100 cm²) = 10 cm.

Therefore, the length of one side of the rhombus is 10 cm.

Now, we can calculate the perimeter using the formula: Perimeter = 4 * side. Perimeter = 4 * 10 cm = 40 cm.

Therefore, the perimeter of the rhombus is 40 cm.

To summarize: - The area of the rhombus is 192 cm². - The perimeter of the rhombus is 40 cm.

Let me know if there's anything else I can help you with!