Rhombus Example Questions
Let’s solve some example questions on Rhombus and its properties.
Example 1: MNOP is a rhombus. If diagonal MO = 29 cm and diagonal NP = 14 cm, What is the area of rhombus MNOP?
Solution:
Area of a rhombus = (d1)(d2)/2
Substituting the lengths of diagonals in the above formula, we have:
A = (29)(14)/2 = 406/2 = 203 cm2
Area of rhombus MNOP = 203 cm2
Example 2: ABCD is a rhombus. The perimeter of ABCD is 40, and the height of the rhombus is 12. What is the area of ABCD?
Solution:
Perimeter = 40 cm
Perimeter = 4 × side
40 = 4×side
⇒ side(base) = 10 cm
and height = 12 cm (given)
Now, Area of Rhombus = base × height
⇒ Area = 10×12 = 120 cm2
Thus, Area of rhombus ABCD is equal to 120 cm2
Example 3: Find the area of a rhombus with diagonal lengths of (2x+2) and (4x+4) units.
Solution:
We know, Area of a rhombus = (d1)(d2)/2
Substituting the lengths of diagonals in the above formula, we have:
A = \frac{(2x+2)(4x+4)}{2}
⇒ A = \frac{\sqrt{8x^2}}{2}
⇒ A = \frac{8x^2+16x+8}{2}
⇒ A = (4x2 + 8x + 4) unit2
Example 4: Find the area of a rhombus if its diagonal lengths are \sqrt{2x} cm and \sqrt{4x} cm.
Solution:
We know, Area of a rhombus = (d1)(d2)/2
Substituting the lengths of diagonals in the above formula, we have:
A = \frac{\sqrt{2x}\sqrt{4x}}{2}
⇒ A = x\sqrt{2} cm2
Rhombus: Definition, Properties, Formula and Examples
Rhombus is a quadrilateral with all four sides equal and opposite sides parallel to each other. The opposite angles of a rhombus are equal. Any rhombus can be considered a parallelogram, but not all parallelograms are rhombus.
Let’s know more about Rhombus and it’s properties, examples and formula in detail below.