Rhombus is a 2-D plane figure with a closed shape.
All sides of a rhombus are equal.
Rhombus is a type of parallelogram.
A rhombus can also known as diamond, rhomb, and lozenge.
Area of Rhombus
In fig., ABCD is a rhombus and AC and BD are its diagonals.
Diagonal BD divides the rhombus ABCD into two congruent triangles DCB and DAB.
Area of ABCD = Area of triangle DCB + Area of triangle DAB
= 1\2 x DB x OC + 1\2 x DB x OA
= 1\2 x DB x (OC + OA)
= 1\2 x DB x AC
We can find the area of the rhombus in many ways, which is given below.
1. Area of Rhombus using height and Base
When the height h and the length of the sides b, the area of a rhombus is given by the formula;
Area of rhombus = base × height
A = b × h
2. Area of Rhombus Using Diagonals
Area of Rhombus = ½ × d1 × d2
Where d1 and d2 are the diagonals of a rhombus.
3. Area of Rhombus using the Length of the Sides and Angle.
The area of a rhombus is equal to the multiple side length squared and the sine of the angle between the two sides.
Area of rhombus = b2 × Sine (A)
Where A = angle formed between two sides of a rhombus
Find the area of a rhombus!!
Find the area of a rhombus whose side is 40 cm and height is 25 cm.
As we know the area of a rhombus A = b × h
= (40 x 25) cm2
= 1000 cm2
If the height and area of a rhombus are 9 cm and 54 cm2, respectively, find the rhombus’s dimensions.
A = b × h
54 cm2 = 8 cm x b
Divide both sides by 8.
54 cm2/9 cm = b
b = 6 cm.
Therefore, the dimensions of the rhombus are 6 cm by 6 cm.
The two diagonals of a rhombus are 10 cm and 12 cm. find the rhombus area.
Let d1 = 10 cm and d2 = 12 cm.
A = ½ × d1 × d2
= (½ × 10 × 12) cm2.
= 60 cm2.
Find the area of a rhombus whose sides are 7 cm, and the angle between the two sides is 90 degrees.
Area of a rhombus = b2 × Sine (A)
= 72 x sine (60)
= 49 cm2.