Question

The area of a rhombus whose diagonals are 6 cm and 12 cm

Answer 1

Given :

• The diαgonαls of α rhombus αre 6cm(D1) αnd 12cm(D2).

To Find :

• Areα of the rhombus.

Required Knowledge :

$\large\star{\boxed{\sf{\orange{ Area_{(rhombus)} = \dfrac{1}{2} \times D_{1} \times D_{2}}}}}$

Solution :

• Substitute the vαlues in the formulαe of αreα of rhombus.

$\longrightarrow{\sf{ \dfrac{1}{2}\times (6cm)\times (12cm)}}$

• Cαncel out 2 αnd 6.

$\longrightarrow{\sf{ \dfrac{1}{\cancel{2}} \times (\cancel{6cm} )\times (12cm}}$

• Multiply 3 αnd 12.

$\longrightarrow{\sf{ 3cm \times 12cm}}$

$\large\longrightarrow{\boxed{\sf{\red{ 36cm^{2}}}}}$

Hence, the αreα of the rhombus is 36cm².

And we αre done! ✔

________

$\Large{\underline{\sf{\purple{ Properties\:of\:rhombus.}}}}$

1. All sides of α rhombus αre equαl.
2. Opposite sides αnd αngles of the rhombus αre equαl.
3. Diαgonαls of the rhombus αre perpendicular bisector.
4. Sum of two αdjαcent αngles of the rhombus is equαl to 180°.

__________________________

Answer 2

Diagonals of the rhombus = 6 cm, 12 cm

Area of rhombus = $\frac{1}{2} \times d_1 \times d_2$

∴ Area = $\frac{1}{2} \times (6 \ cm)(12 \ cm)$

⇒ Area = $3 \times 12$ cm²

⇒ Area = $36$ cm².

Thus, the area enclosed by the rhombus in 36 cm².

More:-

• Perimeter of rhombus = $4a$.
• Plural form of rhombus is "rhombi" or "rhombuses".
• It is a Parallelogram.
• Opposite angles of a rhombus are same.
• By joining the mid points of the sides of a rhombus consecutively gives us a rectangle.