Question

The perimeter of a rhombus is40 cm. one of the diagonal is 12 cm.find area of rhombus​

Answer 1

Given :-

Perimeter of the rhombus = 40 cm

One of the diagonal of the rhombus = 12 cm

Formula to be used :-

Perimeter of the rhombus = 2 $\sqrt{(First\:\:Diagonal)^{2} + (Second\:\:Diagonal)^{2}}$

Area of the rhombus = $\frac{First\:\:diagonal \times Second\:\:diagonal}{2}$

Solution :-

Perimeter of the rhombus = 2 $\sqrt{(First\:\:Diagonal)^{2} + (Second\:\:Diagonal)^{2}}$

$\star$ Substituting the values

=> 40 cm = 2$\sqrt{(12\:cm)^{2} + (Second\:\:Diagonal)^{2}}$

=> $\frac{40\:cm}{2} = \sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}}$

=> 20 cm = $\sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}}$

[Squaring both the sides.]

=> (20 cm)² = $( \sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}})^{2}$

=> 400 cm² = $144\:cm^{2} + (Second\:\:Diagonal)^{2}$

=> 400 cm² - 144 cm² = (Second Diagonal)²

=> 256 cm² = (Second Diagonal)²

[Multiplying both the sides with square roots]

=> $\sqrt{256\:cm^{2} }$ = Second diagonal

=> 16 cm = Second Diagonal

Now,

Area of the rhombus

$=\frac{First\:\:diagonal \times Second\:\:diagonal}{2}= \frac{12\:cm \times 16\:cm}{2}= \frac{192\:cm^{2} }{2}= 96 \:cm^{2}$

Answer :-

Area of the rhombus with perimeter 40 cm, one diagonal 12 cm and second diagonal 16 cm is 96 cm².

Answer 2

Given :-

• Perimeter of the rhombus = 40 cm
• One of the diagonal of the rhombus = 12 cm

Formula to be used :-

Perimeter of the rhombus = 2 $\sqrt{(First\:\:Diagonal)^{2} + (Second\:\:Diagonal)^{2}}$

Area of the rhombus = $\frac{First\:\:diagonal \times Second\:\:diagonal}{2}$

Solution :-

Perimeter of the rhombus = 2 $\sqrt{(First\:\:Diagonal)^{2} + (Second\:\:Diagonal)^{2}}$

$\star$ Substituting the values

=> 40 cm = 2$\sqrt{(12\:cm)^{2} + (Second\:\:Diagonal)^{2}}$

=> $\frac{40\:cm}{2} = \sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}}$

=> 20 cm = $\sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}}$

[Squaring both the sides.]

=> (20 cm)² = $( \sqrt{144\:cm^{2} + (Second\:\:Diagonal)^{2}})^{2}$

=> 400 cm² = $144\:cm^{2} + (Second\:\:Diagonal)^{2}$

=> 400 cm² - 144 cm² = (Second Diagonal)²

=> 256 cm² = (Second Diagonal)²

[Multiplying both the sides with square roots]

=> $\sqrt{256\:cm^{2} }$ = Second diagonal

=> 16 cm = Second Diagonal

Now,

Area of the rhombus

$=\frac{First\:\:diagonal \times Second\:\:diagonal}{2}= \frac{12\:cm \times 16\:cm}{2}= \frac{192\:cm^{2} }{2}= 96 \:cm^{2}$

Hence;

Area of the rhombus with perimeter 40 cm, one diagonal 12 cm and second diagonal 16 cm is 96 cm².