Question

4)If the perimeter of rhombus is 100 cm and length of one of the diagonal is 48 cm, what is the
area of the rhombus?​

Answer 1

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Answer:}}}}}$

The area of quadrilateral is 336 cm².

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Step\:-by-\:step \:explanation:}}}}}$

A rhombus has four equal sides. The perimeter of a rhombus is 100 cm.

$\sf\color{magenta}{4a\:=\:100}$

$\sf\color{magenta}{a=25}$

$\mathbb{The\: measure\: of\: each \: \: side\: is \: 25}$

$4a^2=d_1^2+d_2^24a$

$\mathbb{Where\: , a \: is \: side\: length \: and \: d₁ \: and\: d₂ \: are\: diagonals}$

$4(25)^2=(48)^2+d_2^24(25)$

$d_2=\sqrt{2500-2304}$

$\mathbb{The\: area\: of\: rhombus\: is}$

$A=\frac{1}{2}(d_1d_2)$

$A=\frac{1}{2}\times 48\times 14$

$\tt{A=336}$

$\textbf\color{magenta}{Therefore the area of quadrilateral is 336 cm².}$

More to know :-

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}$

Note :-

~Scrooll to see full answer