Question

Знайдіть площу ромба, якщо його менша діагональ і сторона дорівнюють 4м.

Answer 1

Диагонали точкой пересечения делятся пополам, найдём половину другой диагонали по теореме Пифагора:
4²=2²+а²
16=4+а²
а²=12
а=2кореньиз3
2. S=(d1d2)/2
d1=4 d2=4 кореньиз3
S=(4×4кореньиз3):2=8кореньиз3 м²

Answer 2

Finding the Area of a Rhombus

To find the area of a rhombus, you need to know the length of one of its diagonals and the length of one of its sides. In this case, the length of the smaller diagonal is given as 4 meters.

The formula to calculate the area of a rhombus is:

Area = (d1 * d2) / 2

Where: - d1 and d2 are the lengths of the diagonals of the rhombus.

Since only the length of the smaller diagonal is given, we need to find the length of the larger diagonal.

To find the length of the larger diagonal, we can use the fact that the diagonals of a rhombus bisect each other at right angles. This means that the diagonals form four congruent right triangles.

Using the Pythagorean theorem, we can find the length of the larger diagonal:

d2 = 2 * √(s^2 - (d1/2)^2)

Where: - s is the length of one side of the rhombus.

In this case, the length of one side is also given as 4 meters.

Let's calculate the length of the larger diagonal first:

d2 = 2 * √(4^2 - (4/2)^2) = 2 * √(16 - 4) = 2 * √12 = 2 * 2√3 = 4√3

Now that we have the lengths of both diagonals, we can calculate the area of the rhombus:

Area = (4 * 4√3) / 2 = 8√3 square meters

Therefore, the area of the rhombus with a smaller diagonal of 4 meters and a side length of 4 meters is 8√3 square meters.