Question

8. Знайдіть площу ромба, периметр якого 100 см, а одна з діагоналей 40 см.

Answer 1

Ответ:

Объяснение:

Дано:

Р = 100 см

d = 40 см

Знайти: S -?

Сторона ромба  а = P/4 = 100/4 = 25 (см)

Діагоналі в ромбі перетинаються під прямим кутом, а ділять один одного навпіл.

Нехай довжина  діагоналі  2d1 = 40 (см) , тоді d1 = 40 : 2 = 20 (см)., а  другої діагоналі 2d2

Згідно т. Піфагора

а² = (d1)² + (d2)² =>

d2= √25² - 20² = √625 - 400 = √225 = 15( см)

Площа ромба дорівнює: S = 1/2 d1 *d2 = 1/2 * 20 * 15 = 150(см²)

Answer 2

Finding the Area and Perimeter of a Rhombus

To find the area and perimeter of a rhombus, we need to know the length of one of its diagonals and the perimeter. In this case, we are given that the perimeter of the rhombus is 100 cm and one of its diagonals is 40 cm.

Let's start by finding the length of one side of the rhombus. Since the perimeter is the sum of all four sides, we can divide the perimeter by 4 to get the length of one side:

Perimeter = 4 * Side Length

Given that the perimeter is 100 cm, we can solve for the side length:

100 cm = 4 * Side Length

Dividing both sides by 4, we find:

Side Length = 100 cm / 4 = 25 cm Now that we know the length of one side, we can find the area of the rhombus. The area of a rhombus can be calculated using the formula:

Area = (Diagonal 1 * Diagonal 2) / 2

In this case, we are given that one of the diagonals is 40 cm. To find the other diagonal, we can use the properties of a rhombus. In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right triangles. The length of one diagonal can be found using the Pythagorean theorem:

Diagonal 1 = sqrt((Side Length/2)^2 + (Side Length/2)^2)

Substituting the value of the side length (25 cm) into the formula, we get:

Diagonal 1 = sqrt((25 cm/2)^2 + (25 cm/2)^2) = sqrt(12.5^2 + 12.5^2) = sqrt(312.5 + 312.5) = sqrt(625) = 25 cm Since the diagonals of a rhombus are equal in length, we can conclude that the other diagonal is also 25 cm.

Now we can calculate the area of the rhombus:

Area = (Diagonal 1 * Diagonal 2) / 2 = (25 cm * 25 cm) / 2 = 625 cm^2 Therefore, the area of the rhombus is 625 cm^2 and the length of one side is 25 cm.