Rhombus

A rhombus is a type of quadrilateral which has the following properties:

1. Equal Sides: All four sides of a rhombus are of equal length. This means that the opposite sides are parallel and congruent.
2. Opposite Angles: The opposite angles of a rhombus are equal in measure.
3. Diagonals: The diagonals of a rhombus bisect each other at right angles and are of equal length.

Formulas and Properties:

Here are some important formulas and properties related to rhombuses:

• Perimeter: The perimeter of a rhombus is given by P = 4 * side length.
• Area: The area of a rhombus can be calculated using the formula A = (diagonal 1 * diagonal 2) / 2.
• Diagonal Length: The length of the diagonals can be found using the Pythagorean theorem: d = sqrt((side length)^2 + (side length)^2).

Example Problems:

Let's solve some example problems to understand the concepts better:

1. Problem 1: Find the area of a rhombus with side length 6 cm and diagonals 8 cm and 10 cm.

Solution: Using the formula A = (diagonal 1 * diagonal 2) / 2, we get A = (8 * 10) / 2 = 40 square cm.

2. Problem 2: If the perimeter of a rhombus is 24 cm, find the length of each side.

Solution: Given P = 4 * side length, we have 24 = 4 * side length. So, side length = 24 / 4 = 6 cm.

Practice Questions:

Now, it's time to practice some questions to reinforce your understanding. Try solving the following problems:

1. Find the perimeter of a rhombus with side length 12 cm.
2. If the diagonals of a rhombus are 16 cm and 30 cm, find the area of the rhombus.

Hope this study guide helps you understand the concept of rhombus better. Good luck with your practice questions!