Sample Questions – Is every rectangle a rhombus

Question 1. Calculate the area of a rectangular frame, which has 6 inches in length and is 3 inches wide. 

Solution:

Since, we know, 

Area of a Rectangle = (Length × Width) square units.

Substituting the values, we obtain, 

the area of rectangular frame = 6 × 3 = 18 square inches

Question 2. Find the length of diagonal of a rectangle which has length as 12 cm and width, 8 cm respectively. 

Solution:

We know,

Diagonal Length, 

D = [Tex]\sqrt{ L^2+W^2}[/Tex]

⇒ D = [Tex]\sqrt{12^2+8^2}[/Tex]

⇒ D = [Tex]\sqrt{144 + 64}[/Tex]

⇒ D = √208

⇒ D = 4√3

Question 3. Find the area of a rhombus with the two diagonal lengths d₁ and d₂ to be 6cm and 12 cm, respectively. 

Solution:

We have, 

Diagonal d₁ = 6cm

Diagonal d₂= 12 cm

Area of the rhombus is given by,

A = [Tex] \frac{(d_1 \times d_2)}{2}[/Tex] sq. units

A = [Tex]\frac{( 6 \times 12)}{2}[/Tex]

A = [Tex]\frac{72}{2}[/Tex]

A = 36 cm²

Therefore, the area of rhombus = 36 cm².

Question 4. Difference between Rhombus and Rectangle?

Solution:

Is every rectangle a rhombus? Rectangle is a two-dimensional geometrical figure depicted by four sides and four corners. A rectangle contains sides such that the length of the opposite sides is equal and these sides are parallel to each other. The sides sharing a corner from adjacent sides with an angle of 90° between them. Therefore, there are four right angles in the rectangle.