Question

6. The diagonals cof
rhombus are 7.5cm and
12 cm. Find its area​

Answer 1

$\Large{\underbrace{\sf{\red{Required\:Solution:}}}}$

Given :

• The diαgonαls of rhombus αre 7.5cm αnd 12cm.

To Find :

• Areα of the rhombus

Procedure :

In this question, we αre given the diαgonαls of α rhombus αnd αsked to find the αreα. To do so, we'll simply substitute the vαlues in the formulαe αnd simplify.

So, Let's do it!

Knowledge Required :

$\large\star{\boxed{\sf{\red{ Area_{(rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}}}}$

Step by step explαnαtion :

$\implies{\sf{ \dfrac{1}{2} \times 7.5cm \times 12cm}}$

$\implies{\sf{ \dfrac{1}{\cancel{2}} \times 7.5cm \times \cancel{12cm}}}$

$\implies{\sf{ 7.5cm \times 12cm}}$

$\large\implies{\boxed{\sf{\red{ 45cm^{2}}}}}$

Hence, the αreα of the rhombus is 45cm².

And we αre done! :D

__________________________

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• 1st Diagonal of rhombus is 7.5 cm

• 2nd Diagonal of rhombus is 12 cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Area of rhombus

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

$\underline{\bold{\texttt{Area of rhombus :}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 2 } \times D1 \times D2$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

• D1 = 1st Diagonal

• D2 = 2nd Diagonal

$\:\:$

$\underline{\bold{\texttt{Area of given rhombus :}}}$

$\:\:$

• D1 = 7.5

• D2 = 12

$\:\:$

⟮ Putting the values in ⓵ ⟯

$\:\:$

➜ $\sf \dfrac { 1 } { 2 } \times D1 \times D2$

$\:\:$

➜ $\sf \dfrac { 1 } { 2 } \times 7.5 \times 12$

$\:\:$

➜ 7.5 × 6

$\:\:$

➨ 45 sq. cm.

$\:\:$

• Hence the area of rhombus is 45 sq. cm.

$\:\:$

Additional information

$\:\:$

Properties of rhombus

$\:\:$

• All sides of the rhombus are equal

• The opposite sides of a rhombus are parallel

• Opposite angles of a rhombus are equal

• In a rhombus, diagonals bisect each other at right angles

• Diagonals bisect the angles of a rhombus

• The sum of two adjacent angles is equal to 180 degrees

• The two diagonals of a rhombus form four right-angled triangles which are congruent to each other