rhombus
A rhombus is a special type of quadrilateral (a polygon with four sides)
A rhombus is a special type of quadrilateral (a polygon with four sides). It is also known as a diamond shape or a lozenge.
Properties of a Rhombus:
1. All four sides of a rhombus are congruent, which means they have equal lengths.
2. Opposite sides of a rhombus are parallel to each other.
3. Opposite angles of a rhombus are equal, and the sum of any two adjacent angles is always 180 degrees.
4. The diagonals of a rhombus bisect each other at right angles. This means that they divide each other into two equal parts and the angle between them is 90 degrees.
Formulas for a Rhombus:
1. Perimeter: The perimeter of a rhombus can be found by multiplying the length of one side by 4.
Perimeter = 4 * side length.
2. Area: The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing the result by 2.
Area = (diagonal 1 * diagonal 2) / 2.
3. Diagonal Length: If the lengths of the diagonals of a rhombus are known, the length of each diagonal can be found using the Pythagorean theorem.
Diagonal Length = √(side length^2 + side length^2).
Example:
Let’s say we have a rhombus where each side measures 5 cm and one diagonal measures 8 cm. We can find the length of the other diagonal using the Pythagorean theorem.
Using the diagonal length formula:
Diagonal Length = √(5^2 + 5^2)
Diagonal Length = √(25 + 25)
Diagonal Length = √50 cm
So, the length of the other diagonal is approximately 7.07 cm.
To find the area of the rhombus:
Area = (8 cm * 7.07 cm) / 2
Area = 56.56 cm^2
Therefore, the area of the given rhombus is 56.56 square centimeters.
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