Question

The area of rhombus is 16 cm^2 and lenght of one of its diagonals is 4 cm. calculate the lenght of other diagonal. also find the side of the rhombus.explain it in steps​

Answer 1

$\sf\purple{Given :-}$

• $\rm\green{Area\:=\:16cm^2}$
• $\rm\green{One\:of\:its\:diagonal\:=\:4cm}$
• $\rm\green{Other\:Diagonal\:=\:?}$

$\sf\purple{To \:Find :-}$

• $\rm\green{Other\:Diagonal}$

$\sf\purple{Solution :-}$

$\sf\blue{The\:formula\:used}$ = ${\sf{\underline{\boxed{\red{\sf{Area\:=\frac{1}{2}×d_1×d_2}}}}}}$

$\rm\blue{Here\:,}$

Area = $\sf\green{16cm^2}$

$\rm\blue{1st \:diagonal =}$ $\sf\green{4cm}$

$\rm\blue{2nd\: diagonal = }$

$:\implies\sf{\frac{1}{2}×4cm×d_2}= 16cm^2$

$:\implies\sf{2cm×d_2}= 16cm^2$

$:\implies\sf{d_2 =\frac{16cm^2}{2cm}}$

$:\implies\sf{d_2 =\frac{\cancel16cm^2}{\cancel2cm}}$

$:\implies\sf{d_2 = 8cm\:Ans\:!}$

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$\sf\purple{Keep\:in\:mind}$

Formulas to Calculate Area of Rhombus :-

$\rm\green{Using\:diagonals =}$$\sf{\boxed{\red{\sf{Area\:=\frac{1}{2}×d_1×d_2}}}}$

$\rm\green{Using\:base\:and\:height =}$ $\sf{\boxed{\red{\sf{Area\:=B × H}}}}$

$\rm\green{Using\:Trignometry =}$$\sf{\boxed{\red{\sf{Area\:=b^2×sin(a)}}}}$

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