# How to find a diamond side?

Irina Cheverda

October 15, 2014

## Watch the video

How to find a diamond side?

A rhombus is an equilateral parallelogram.

## Diamond properties:

- the diagonal is a bisector;
- diagonals intersect at a point that divides them in half. The angle of intersection is 90 degrees;
- opposite sides are parallel to each other;
- if the diamond has right angles, then this is a square.

## Basic formulas:

The area of a diamond S can be found by the following formulas:

- S = ah
- S = 2 · r · a, where r is the radius of the circle inscribed in the diamond, and is the side of the diamond.
- S = (d1 · d2) / 2, where d1 and d2 are diagonal diamonds;

where:

- a - side of the diamond;
- h - height;
- d1 and d2 are diagonals;
- r is the radius of the inscribed circle;

## How to find a diamond side?

If we need to find a rhombus side, then this can be done in several ways. Consider an example. Dan a diamond ABCD. Its diagonals are AC and BD:

- We consider the unknown side as the hypotenuse of a right-angled triangle (half of the diagonals of the rhombus are the legs of this triangle).We recall the Pythagorean theorem and find the right side. Namely, the sum of the squares of the half diagonal of the rhombus will be equal to the square of the desired side.
- AB2= AA2+ BО2.

- If you know the area of a rhombus and one of its corners, then you can look for a side using the formula:
- S = a2sinα
- Where: a - side of the diamond;
- α is the known angle between the sides.
- From the previous formula we deduce that the rhombus side can be calculated using the formula: a = √ (S / sinα)

- In the case when only the diagonals are known, the side can be found by the formula:
- a = (√D2+ d2)/2
- Where:
- D is the large diagonal of the rhombus;
- d is the smaller diagonal of the rhombus.

### Example of solving the problem:

Find the side of the diamond. It is known that its diagonals are equal to 20 and 48 cm.

- a = (√D2+ d2)/2
- a = (√482+202)/2
- a = (√ 2704) / 2
- a = 26

Based on the properties of a rhombus, we find that the sides are equal to each other and equal to 26 cm.