Question

Perimeter of equilateral triangle 42cm find area of triangle

Answer 1

perimerter of equilateral triangle= 42cm

.°. its sides= 42 /3 cm

= 14 cm

area of traingle= (root 3 /4) (side)^2

= (root 3/4 )×(14 cm)^2

= 6.062 cm^2

Answer 2

$\huge \bold {\underline{\fbox{Correct \: Question:- }}}$

$\sf {{If \: perimeter \: of \: equilateral \: triangle \: is \: 42cm, \: find \: area \: of \: triangle.}}$

$\huge \bold {\underline {\fbox{Answer:-}}}$

$\bold {Given:} \\ \sf \implies{Perimeter \: of \: equilateral \: triangle \: is \: 42cm.} \\ \bold{To \: find:} \\ \sf \implies{Area \: of \: equilateral \: triangle.} \\ \bold{Concept \: used:} \\ \sf \implies{Sides \: of \: a \: equilateral \: triangle \: are \: always \: equal.} \\ \bold{Formula \: used:} \\ \sf \implies{Perimeter \: of \: equilateral \: triangle=sum \: of \: all \: sides} \\\sf \implies{Area \: of \: equilateral \: triangle=\frac{ \sqrt{3}}{4} {a}^{2}} \\ \sf{where,}\\ \sf{•a \: is \: the \: side \: of \: a \: triangle.} \\ \large\bold{According \: to \: Question:} \\ \tt{First \: we \: find \:sides \: of \: triangle.} \\ \sf{∵Perimeter \: of \: triangle=a+b+c} \\ \sf{∴42cm=3a \: \: \: (∵sides \: of \: equilateral \: triangle \: is \: equal.)} \\ \sf{∴ \frac{42}{3} = 14} \\ \sf \implies{Hence,sides \: of \: equilateral \: triangle \: is \: 14cm.} \\ \sf{Then,} \\ \sf{Area \: of \: triangle= \frac{ \sqrt{3} }{4} {a}^{2} = \frac{ \sqrt{3} }{4} {14}^{2} = \frac{ \sqrt{3} }{4} \times 196 = \sqrt{3} \times 49 =84.87}$

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