Question

a Rhombus, length of the one diagonal is 6 cm, another diagonal is thrice the other.
its area is
14 cm
28 cm
22 cm
54cm​

Answer 1

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

$\sf In \: a \: rhombus,$

$\sf \Rrightarrow Length \: of \: one \: diagonal = 6 \: cm.$

$\sf \Rrightarrow Another \: diagonal \: length \: is \: thrice \: of \: other.$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Area \: of \: rhombus = \: ?$

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

$\underline{ \boxed{ \sf {Area\:of\:Rhombus} = \dfrac{1}{2} \times (d_1 \times d_2)}}$

$\sf In \: the \: formula,$

$\sf \implies d_1 = Length \: of \: first \: diagonal$

$\sf \implies d_2 = Length \: of \: second \: diagonal$

$\bf \underline{Now},$

$\sf \implies Length \: of \: first \: diagonal \: (d_1) = \bf 6 \: cm$

$\sf \implies Length \: of \: second \: diagonal \: (d_2) = \bf 3 \times 6 = 18 \: cm$

$\sf Substitute \: the \: values,$

$\sf \implies {Area\:of\:Rhombus} = \dfrac{1}{ \cancel{2}} \times ( \cancel{6 }\times 18)$

$\sf \implies {Area\:of\:Rhombus} = 3 \times 18$

$\sf \implies{Area\:of\:Rhombus}=54 \: cm^{2}$

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$\bf More\: formulas\:based \: on \: area :$

$\bf{1.} \: \sf Area \: of \: triangle = \dfrac{1}{2} \times (Base \times height )$

$\bf{2.} \: \sf Area \: of \: square = (Side)^2$

$\bf{3.} \: \sf Area \: of \: rectangle = Length \times Breadth$

$\bf{4.} \: \sf Area \: of \: trapezium = \dfrac{1}{2} \times (Sum \: of \: two \: bases ) \times height$