Question

perimeter of rhombus is 20cm.
if one of its diagonal is 10cm. Find its area ¿¿​

Answer 1

$\bf{\underline{\underline{ \bigstar \bigstar\: Figure : }}}$

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$\setlength{\unitlength}{1.6mm}\begin{picture}(5,6)\put(0,0){\line(1,1){12}}\put(20,0){\line(1,1){12}}\put(0,0){\line(1,0){20}}\end{picture}\put(6.8,12){\line(1,0){20}}\put(15,0){\line(-2,3){8}}\put(5,3){}\put(4.5,-2){}\put(11,7.5){10cm}$

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$\bf{\underline{\underline{ \bigstar \bigstar\: Given : }}}$

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• $\footnotesize{ Perimeter\: of\: rhombus = 20cm}$

• $\footnotesize{ Diagonal\: of\: rhombus = 10cm}$

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$\bf{\underline{\underline{ \bigstar \bigstar\: To\:Find : }}}$

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• $\footnotesize{ Area\: of\: rhombus }$

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$\bf{\underline{\underline{ \bigstar \bigstar\: Solution : }}}$

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$\footnotesize{ Perimeter\: of\: rhombus = 20cm}$

$\footnotesize{\implies Side × 4 = 20cm}$

$\footnotesize{\implies Side = \dfrac{20cm}{4} }$

$\footnotesize{\implies Side = 5cm}$

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$\rule{200}3$

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$\footnotesize{ Area\: of\: rhombus = \dfrac{1}{2}d \sqrt{ {4 a}^{2} - {d}^{2}} }$

$\footnotesize{ Area\: of\: rhombus = \dfrac{1}{2} \times 10cm \sqrt{ {(4 \times 5cm)}^{2} - {(10cm)}^{2} }}$

$\footnotesize{ Area\: of\: rhombus = 5cm \sqrt{ {20cm}^{2} - {100cm}^{2} }}$

$\footnotesize{ Area\: of\: rhombus = 5cm \sqrt{ {400cm}^{2} - {100cm}^{2} }}$

$\footnotesize{ Area\: of\: rhombus = 5cm \sqrt{ {300cm}^{2}} }$

$\footnotesize{ Area\: of\: rhombus = 5cm \times 17.32cm }$

$\footnotesize{ Area\: of\: rhombus = {86.60cm}^{2} }$

Answer 2

Rhombus = all sides are equal .

Perimeter = sum of all sides

perimeter of rhombus = 20

x+x+x+x = 20

4x= 20

x= 20/4

x= 5

Therefore , one side of a rhombus is 5cm .

AREA OF RHOMBUS = 1/2 × 10 × 10

= 50 cm

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