Question

Площадь ромба равна 48 квадратных сантиметров. Найдите площадь четырёхугольника, вершинами которого являются середины сторон этого ромба. Подробно, если можно. Заранее спасибо!

Answer 1

S ромба=48=(1/2)*d1*d2; => d1*d2=96
S=(1/2)*(1/2)d1*(1/2)d2=(1/8)*d1*d2=96/8= 12
BD=sqrt(400-144)=16; AD^2=BD*CD; => CD=144/16=9; => BC=25

Answer 2

Finding the Area of the Quadrilateral

To find the area of the quadrilateral with vertices at the midpoints of the sides of the given rhombus, we can use the fact that the diagonals of a rhombus bisect each other at right angles, creating four congruent right-angled triangles.

Let's denote the length of the diagonals of the rhombus as d1 and d2. The area of the rhombus can be expressed as (d1 * d2) / 2. Given that the area of the rhombus is 48 square centimeters, we can find the length of the diagonals using this information.

Calculating the Diagonals of the Rhombus

Using the formula for the area of a rhombus, we can solve for the length of the diagonals: 48 = (d1 * d2) / 2

Solving for the diagonals, we get: d1 * d2 = 96

Finding the Length of the Diagonals

To find the length of the diagonals, we can use the fact that the diagonals of a rhombus bisect each other at right angles, creating four congruent right-angled triangles. Therefore, the length of the diagonals can be found using the Pythagorean theorem.

Let's denote the length of the sides of the rhombus as a. Then, the length of the diagonals can be expressed as √(a^2 + b^2), where a and b are the lengths of the sides of the rhombus.

Calculating the Length of the Diagonals

Using the given area of the rhombus (48 square centimeters), we can solve for the length of the diagonals: a * b = 96

We can also use the fact that the diagonals bisect each other at right angles to find the length of the diagonals.

Final Steps

Once we have the lengths of the diagonals, we can use them to find the lengths of the sides of the quadrilateral and then calculate its area. If you have the specific lengths of the sides of the rhombus, we can proceed with the calculations to find the area of the quadrilateral.