Question

ОЧЕНЬ СРОЧНО!!!Одна з діагоналей ромба 30 см. Периметр ромба 68 см. Знайти площу ромба.​

Answer 1

Ответ:

240см²

Объяснение:

ABCD- ромб.

Р(ABCD)=4*AB.

AB=P(ABCD)/4=68/4=17см.

ВD=30см.

ВО=ВD/2=30/2=15см.

∆АВО- прямоугольный треугольник.

По теореме Пифагора

АО=√(АВ²-ВО²)=√(17²-15²)=√(289-225)=

=√64=8см.

АС=2*АО=2*8=16см.

S=1/2*BD*AC=1/2*30*16=240см²

Answer 2

Calculation of the Area of a Rhombus

To find the area of a rhombus, we need to know the length of one of its diagonals. In this case, we are given that one of the diagonals of the rhombus is 30 cm.

The formula to calculate the area of a rhombus is:

Area = (diagonal1 * diagonal2) / 2

Since a rhombus has two diagonals of equal length, we can use the given diagonal length to find the area.

Let's calculate the area using the given information:

Diagonal1 = 30 cm

Perimeter = 68 cm

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

The perimeter of a rhombus is the sum of the lengths of all four sides. Since all four sides of a rhombus are equal, each side length is equal to the perimeter divided by 4.

Side length = Perimeter / 4 = 68 cm / 4 = 17 cm

Now, we can use the Pythagorean theorem to find the length of the other diagonal.

In each right-angled triangle formed by the diagonals, one side is half the length of a side of the rhombus (which is half the side length we just calculated) and the hypotenuse is the length of one of the diagonals (which is 30 cm).

Using the Pythagorean theorem, we can calculate the length of the other side of the right-angled triangle (which is half the length of the other diagonal):

Other side of the right-angled triangle = sqrt(diagonal^2 - (side/2)^2)

Other side of the right-angled triangle = sqrt(30^2 - (17/2)^2) = sqrt(900 - 144.5) = sqrt(755.5) ≈ 27.5 cm

Since the diagonals of a rhombus are perpendicular bisectors of each other, the length of the other diagonal is twice the length of the other side of the right-angled triangle.

Diagonal2 = 2 * Other side of the right-angled triangle = 2 * 27.5 cm = 55 cm

Now, we can substitute the values of the diagonals into the formula to calculate the area of the rhombus:

Area = (Diagonal1 * Diagonal2) / 2 = (30 cm * 55 cm) / 2 = 1650 cm²

Therefore, the area of the rhombus is 1650 cm².

Please note that the given search results did not provide any relevant information for this specific question. The calculation and explanation provided above are based on the properties and formulas of a rhombus.