Question

a square of side 1 cm is cut out of
the corner of a larger square with side 3 cm (see the figure), what will be the perimeter of the remaining shape?​

Answer 1

$ABCD\: is \:a \: square.$

$AB = BC = CD = DA = 3 \:cm\:--(1)$

/* If a square EDGF of side 1 cm is cut of out of ABCD */

$In \:EDGF , \\\orange {FE} = \pink {GF} = \orange {GD} = \pink {ED} = 1 \:cm\:--(2)$

$Perimeter \: of \: remaining \\shape \: ABCGFE \\= AB + BC + CG + \pink {GF} + \orange {FE} + EA = \\AB + BC + CG + \pink {ED} + \orange {GD}+ EA$

$[ From \: (2) ]$

$= AB + BC + ( CG + \orange {GD}) + ( AE + \pink {ED})$

$= AB + BC + CD + AD\\= Perimeter \: of \: ABCD \: square \\= 4 \times side \\= 4 \times 3 \\= 12 \:cm$

Therefore.,

$\red{Perimeter \: of \: remaining }$

$\red {shape \: ABCGFE}\green {= 12\:cm }$

Second Method :

$Perimeter \: of \: remaining \\shape \: ABCGFE \\= AB + BC + CG + \pink {GF} + \orange {FE} + EA \\= (3+3+2+1+1+2) cm \\= 12 \:cm \: [From \: figure ]$

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