Question

Find the area of a rhombus having perimeter 80 em and one diagonal 24 em
(1) 354 sq. em (2) 364 sq. em (3) 384 sqem​

Answer 1

$\large{\sf{\underline{\underline\red{Solution!!}}}}$

Given that,

• $\sf{Perimeter\: of\: rhombus = 80 \:cm.}$

• $\sf{First\: diagonal = d_1 = 24 \: cm.}$

We have to find the area and the other diagonal of the rhombus.

• $\sf{Second \:diagonal = d_2 = ?}$

Now,

⇒  $\sf{Perimeter\: of \:the\: rhombus = 4a^2}$

⇒  $\sf{Perimeter = 80 \:cm.}$

⇒  $\sf{80\: cm = 4 a}$

⇒  $\sf{20\:cm = 1a}$

⇒  $\sf{a=20\:cm}$

To find the second diagonal :-

$:\implies\:\sf{4a^2=d_1 \:^2+d_2\:^2}$

$:\implies\:\sf{4\times20\times10=24\times24+d_2\:^2}$

$:\implies\:\sf{1600=576+d_2\:^2}$

$:\implies\:\sf{d_2\:^2=1600-576}$

$:\implies\:\sf{d_2\:^2=1024}$

$:\implies\:\sf{d_2=\sqrt{ 1024}}$

$:\implies\:\sf{d_2=32\:cm}$

Now,

To Find Area of rhombus :-

$:\implies\:\sf{\dfrac{1}{2} \times d_1 \times d_2}$

$:\implies\:\sf{\dfrac{1}{2} \times 24 \times 32}$

$:\implies\:\sf{12 \times 32}$

$:\implies\:\sf{384 \:cm^2}$

Therefore,

Other diagonal of rhombus = 32 cm.

Area of  rhombus = 384 sq. cm.