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RHOMBUS

Definition

A rhombus is a quadrilateral / parallelogram that has FOUR (4) EQUAL SIDES but not necessarily right angles (90°) like a square or a rectangle.

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A right angle is an internal angle which is equal to 90°.

A drawing showing showing a rhombus with four equal sides that are not at right angles.

NOTE: Because a rhombus is a parallelogram like a rectangle or square, opposite sides are parallel and opposite angles are equal.

INTERESTING FACT:

Any square is a rhombus, but not all rhombuses are squares.

It Is Helpful To Think

It is helpful to think of a RHOMBUS as a SQUARE or a RECTANGLE that has been pushed from a side so that it all sides are equal in length.

A drawing showing a rectangle being "slanted" into a rhombus.

Traditional Formula

AreaRhombus = altitude x S or
AreaRhombus = (d1 x d2)/2

A drawing showing a rhombus with its sides being represent by the symbol S. Also the rhombus altitude being represented by a line from one base to the other base at right angles.

NOTE: The ALTITUDE is the distance at right angles to two sides of a rhombus.

Thinking Inside The Box

If you place a RHOMBUS inside of a box (a rectangle or a square) and then move one of its slanted side to the opposite side, you will get a rectangle or a square.

A drawing showing a rhombus inside of a rectangle  being slanted into a smaller rectangle

If all sides of the rhombus are equal and if you place a RHOMBUS inside of a box (a square but NOT a rectangle) and then fold the right or left side that are separated by a diagonal into the opposite side, you will get a rectangle that is half of the box that it is in.

KEY: Since a rhombus is basically a square that has been slanted, it can still be treated somewhat as a square. So, instead of having to learn another formula (AreaRhombus = altitude × S), simply use the rectangle formula instead.

Example

A rhombus with a altitude of 3 in and a side of 4 in has an area of:

  1. Treat the altitude as the height and S as the width since they are all the same length.
  2. Use the rectangle formula instead (AreaRhombus = height x width).

AreaRhombus = 3 in x 4 in = 12 in2

 

A rhombus with both diagonals of 4 has an area of:

  1. Treat the diagonals as the height and width.
  2. Use the rectangle formula instead (AreaRhombus = height x width).
  3. Divide results by 2.

AreaRhombus = 4 in x 4 in = 16 in2/2 = 8 in2

REFERENCE: See screenshots above for graphic representations.

Memorization Tips

A drawing showing a trapezoid that looks like a cars' windshield or a square or a rectangle that has been "squeezed" from two corners of two sides equally. Also, a rhombus that looks like a square or a rectangle that has been "pushed" from one corner to caue the shape to "slant" on both sides equally.