Question

Construct a rhombus with side of length $5cm$ and an acute angle of ${45}^{\circ }$. The area of the rhombus is: (approx.)

• A. $14.2c{m}^2$
• B. $30.9c{m}^2$
• C. $35c{m}^2$
• D. $17.5c{m}^2$

Answer 1

Answer: (D)

$17.5c{m}^2$

$\Rightarrow$ We know that all sides of rhombus are equal.

$\Rightarrow$ Draw a line segment AB = 5cm.

$\Rightarrow$ Construct an angle ${45}^{\circ }$ at point A.

$\Rightarrow$ Cut off AD = 5cm.

$\Rightarrow$ Take D as a center with radius 5cm, draw an arc.

$\Rightarrow$ Take B as center with radius 5cm, draw an arc meeting previous arc at point C.

$\Rightarrow$ Join BC, CD, AC and BD.

$\Rightarrow$ AC and BD are two diagonals of rhombus $ABCD$

$\Rightarrow$ By measuring diagonals we get,

$\Rightarrow$ $l\left(AC\right)=p=9.2cm$ and $l\left(BD\right)=q=3.8cm$ ---( 1 )

$\Rightarrow$ Area rhombus $ABCD=\frac{p\times q}{2}$

$\Rightarrow$ $\frac{9.2\times 3.8}{2}$ [From ( 1 )]

$\therefore$ Area of rhombus $ABCD=17.48c{m}^2\approx 17.5c{m}^2$.