The area of a rhombus is the total amount of space enclosed by a rhombus in a two-dimensional plane.

Use the Pythagoras theorem to find the second diagonal if we know the length of one diagonal and the side length.įAQs on Area of Rhombus What is the Area of Rhombus?.

The area of a rhombus can be found in three ways: when diagonals are given, when an angle and a side are given, when base and height are given.

Remember that the height is not the same as the length of the side of a rhombus.

⇒ Area of rhombus = 16 × 1/2 = 8 sq yards Solution: As we know, the area of a rhombus = s 2 × sin(30º)Īrea of rhombus = s 2 × sin(30º) = 4 2 × 1/2 Let us use this formula in the following example to find the area of a rhombus.Įxample: What is the area of a rhombus if the length of its side is 4 yards and one of its angles A is 30º? Area of a rhombus using side and angle is given as,Īrea of a Rhombus = side 2 × sin(A), where 'A' is an interior angle. We can use any angle because either the angles are equal or they are supplementary, and supplementary angles have the same sine. We apply the concept of trigonometry while calculating the area when sides and angles are known. ∴ Area of a Rhombus = 1/2 × diagonal 1 × diagonal 2 Formula for Area of Rhombus When Side and Angles Are Known The area of the rhombus ABCD = Area of ∆ ADC + Area of ∆ ABCĪrea of the rhombus = 2 × Area of ∆ ABC -Equation (1) (∵ ∆ ABC congruent to ∆ ADC)Īrea of rhombus = 2 × 1/4 × AC × BD = 1/2 × AC × BD (From (1) and (2))

The opposite angles in the rhombus are equal.

All four sides of the rhombus are congruent.

The other points to be noted about this rhombus are given below: Observe the Rhombus ABCD given above in which E is the point of intersection of two diagonals. The formula which is used to find the area of a rhombus using diagonals is given as,Īrea = (d 1 × d 2)/2, where, d 1 and d 2 are the diagonals of the rhombus.

The area of a rhombus is equal to half the product of the lengths of the diagonals.

⇒ Area of rhombus = 70 inches 2 Formula for Area of Rhombus with Diagonals Solution: The side length of a rhombus = 7 inches, height = 10 inches.Īs we know, Area of rhombus = base × height Let us find the area of a rhombus using this formula.Įxample: Find the area of a rhombus in which the side length is 7 inches and the height of the rhombus is 10 inches. The same rule is applied to the rhombus as well. We know that the area of a parallelogram is calculated by multiplying its base and height. Let us understand the area of rhombus formulas in detail and use them to find the area of a rhombus now.įormula for Area of Rhombus with Base and Height

Picture of rhombus