Rhombus area formula with calculator (original) (raw)

Three different ways to calculate the area of a rhombus are given below, with a formula for each.

Try this Drag the orange dots on each vertexto reshape the rhombus. The area will be continuously calculated using the "base times height" method.

A rhombusis actually just a special type of parallelogram. Many of the area calculations can be applied to them also. Choose a formula based on the values you know to begin with.

1. The "base times height" method

First pick one side to be the base. Any one will do, they are all the same length. Then determine the altitude - the perpendicular distance from the chosen base to the opposite side. The area is the product of these two, or, as a formula: where
b is the length of the base
a is the altitude (height).

Use the calculator below to calculate the area of the rhombus given the base (side) length and altitude (perpendicular height).

Enter any two values and the missing one will be calculated. For example, enter the area and base length, and the height needed to get that area is calculated.

2. The "diagonals" method

Another simple formula for the area of a rhombus when you know the lengths of the diagonals. The area is half the product of the diagonals. As a formula: where
d1 is the length of a diagonal
d2 is the length of the other diagonal

3. Using trigonometry

If you are familiar with trigonometry, there is a handy formula when you know the length of a side and any angle: where
s is the length of any side
a is any interior angle
sin is the sine function
(see Trigonometry Overview)

It may seem odd at first that you can use any angle since they are not all equal. But the angles are either equal or supplementary, and supplementary angles have the same sine.

Other polygon topics

General

• Polygon general definition
• Quadrilateral
• Regular polygon
• Irregular polygon
• Convex polygons
• Concave polygons
• Polygon diagonals
• Polygon triangles
• Apothem of a regular polygon
• Polygon center
• Radius of a regular polygon
• Incircle of a regular polygon
• Incenter of a regular polygon
• Circumcircle of a polygon
• Parallelogram inscribed in a quadrilateral

Types of polygon

• Square
• Diagonals of a square
• Rectangle
• Diagonals of a rectangle
• Golden rectangle
• Parallelogram
• Rhombus
• Trapezoid
• Trapezoid median
• Kite
• Inscribed (cyclic) quadrilateral
  • Inscribed quadrilateral interior angles
  • Inscribed quadrilateral area
  • Inscribed quadrilateral diagonals

Area of various polygon types

• Regular polygon area
• Irregular polygon area
• Rhombus area
• Kite area
• Rectangle area
• Area of a square
• Trapezoid area
• Parallelogram area

Perimeter of various polygon types

• Perimeter of a polygon (regular and irregular)
• Perimeter of a triangle
• Perimeter of a rectangle
• Perimeter of a square
• Perimeter of a parallelogram
• Perimeter of a rhombus
• Perimeter of a trapezoid
• Perimeter of a kite

Angles associated with polygons

• Exterior angles of a polygon
• Interior angles of a polygon
• Relationship of interior/exterior angles
• Polygon central angle

Named polygons

• Tetragon, 4 sides
• Pentagon, 5 sides
• Hexagon, 6 sides
• Heptagon, 7 sides
• Octagon, 8 sides
• Nonagon Enneagon, 9 sides
• Decagon, 10 sides
• Undecagon, 11 sides
• Dodecagon, 12 sides

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