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Area of Rhombus




 
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In this lesson, we will learn different formulas that can be used to calculate the area of a rhombus when we are
  • given a side and height
  • given lengths of the diagonals
  • given a side and an angle


Area of Rhombus

A rhombus has four equal sides and its diagonals bisect each other at right angles.

Given Side and Height

If you are given the length of one side (s) and the perpendicular height (h) from one side to the vertex then the area of the rhombus is equal to the product of the side and height.

The area of the rhombus is given by the formula:

Area of rhombus = sh

This formula for the area of a rhombus is similar to the area formula for a parallelogram.

Given lengths of Diagonals

We can also obtain the area of a rhombus, given the lengths of its diagonals. The area of a rhombus is half the product of its diagonals.

If the lengths of the diagonals are a and b, then area of the rhombus is given by the formula:

Area of rhombus =

The following video shows how to calculate the area of a rhombus given the lengths of the diagonals.

The following video proves that the area of a rhombus is equal to half the product of its diagonals.



Given a Side and an Angle

When given any side and any angle, the area of the rhombus is equal to product of the side squared and the sine of the angle.

Area of rhombus = s2 sin a

where s is the length of any side and a is any interior angle.

We can use any angle because either the angles are equal or they are supplementary, and supplementary angles have the same sine.

Problems using area of rhombus

The following video shows a problem involving the area of a rhombus.

The area of a rhombus is 16 cm2. If one diagonal has a length of 3 cm. Find the length of the other diagonal



 

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