Question

If the lengths of the diagonals of a rhombus are 10 cm and 8 cm then its
area is
80 cm2
40 cm
20 cm​

Answer 1

It is said that the lengths of the diagonals of a rhombus are 10 cm and 8 cm respectively. Then ,

Area of rhombus will be equal to the product of its diagonals divided by 2.

Let's do it :-

${\boxed{\bf{ Area \: of \: rhombus = \dfrac{1}{2} \times d_1 \times d_2 }}}$

• Diagonal 1 → 10 cm

• Diagonal 2 → 8 cm

$\dashrightarrow\:\:\sf Area = \dfrac{1}{2} \times d_1 \times d_2$

$\dashrightarrow\:\:\sf Area = \dfrac{1}{2} \times 10 \times 8$

$\dashrightarrow\:\:\sf Area = \dfrac{1}{2} \times 80$

$\dashrightarrow\:\:\sf Area = \dfrac{80}{2}$

$\sf \longrightarrow \: Area \: = {\dfrac{ \cancel{80}^{ \: \: 40} }{ \cancel{2}^{ \: \: 1} } \: cm^{2} }$

$\dashrightarrow\:\:\sf Area = 40 \: cm^{2}$

Hence,

$\dashrightarrow\:\: \underline{\boxed{\sf Area \: of \: rhombus = 40 \: cm^{2} }}$

Therefore,

Option ( c ) is correct.

➤ Additional Knowledge :-

Formulas to Calculate Area of Rhombus

• Using Diagonals

= ½ × d1 × d2

• Using Base and Height

A = b × h

• Using Trigonometry

= b² × Sin(a)

Answer 2

Given :

If the lengths of the Diagonals of a rhombus are 10 cm and 8 cm

To Find :

Area of the rhombus.

Solution :

We know that,

Area of Rhombus = 1/2 × D₁ × D₂

= 1/2 × 10 × 8

= 1/2 × 80

= 40 cm²

Therefore,

Area of Rhombus is 40 cm²