Question

6. Which of the following has a larger area and by how much?
(1) A rectangle of length 24 cm and breadth 16 cm, or
(ii) A square of side 21 m​

Answer 1

AnswEr :

( 1 ) A Rectangle of Length 24 cm and Breadth 16 cm :

↠ Area of Rectangle = Length × Breadth

↠ Area of Rectangle = (24 cm × 16 cm)

↠ Area of Rectangle = (20 + 4) × 16

↠ Area of Rectangle = 320 cm² + 64 cm²

↠ Area of Rectangle = 384 cm²

_________________________

( 2 ) A square of side 21 m :

↠ Area of Square = (Side)²

↠ Area of Square = (21 m)²

↠ Area of Square = (21 × 100 cm)²

↠ Area of Square = (21 × 21 × 100 × 100)

↠ Area of Square = (441 × 10,000)

↠ Area of Square = 4,410,000 cm²

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• L A R G E R⠀A R E A :

⇒ Larger Area = Square – Rectangle

⇒ Larger Area = 4,410,000 cm² – 384 cm²

⇒ Larger Area = 4,409,616 cm²

• Changing into metre²

⇒ Larger Area = 440.96 m²

∴ Area of Square is Larger & by 440.96 m²

Answer 2

Answer:

$\bold\green{Area\:of\:square\:is\:larger}\bold\red{\:by\:440.9616\:{m}^{2}.}$

Step-by-step explanation:

$\bold{First\:case:-}$

$\bf{Given:-}\begin{cases}\sf{Length\:of\:rectangle=24\:cm}\\\sf{Breadth\:of\:rectangle=16\:cm}\\\sf{Area\:of\:rectangle = ?}\end{cases}$

${\boxed{\bold\red{Area\:of\:rectangle = Length \times Breadth}}}$

$\mapsto\sf Area\:of\:rectangle = (24 \times 16)\:{cm}^{2} \\\\\mapsto{\boxed{\mathfrak\red {Area\:of\:rectangle = 384\:{cm}^{2}}}}$

$\rule{300}{1}$

$\bold{2nd\:case:-}$

$\bf{Given:-}\begin{cases}\sf{Side\:of\:square = 21\:m}\\\sf{Area\:of\:square=?}\end{cases}$

${\boxed{\bold\red{Area\:of\:square ={Side}^{2} }}}$

$\mapsto\sf Side \:of\:square = (21 \times 100)\:cm \\\\\mapsto\sf Side \:of\:square = 2100 \:cm$

$\bigstar\sf Area \:of\:square = {Side}^{2} \\\\\mapsto\sf Area\:of\:square = {2100}^{2} \: {cm}^{2} \\\\\mapsto{\boxed{\mathfrak\red{Area \:of\:square = 4,410,000\:{cm}^{2} }}}$

$\rule{300}{1}$

$\bigstar\sf Larger\:Area = Area \:of\:square - Area\:of\:rectangle \\\\\mapsto\sf Larger\:area = (4410000- 384)\:{cm}^{2} \\\\\mapsto\sf Larger\:area = 4,409,616\:{cm}^{2}$

$\because\sf 1\:{cm}^{2} = \dfrac{1}{100\times 100} \: {m}^{2}$

$\mapsto\sf Larger\:area =\dfrac{4,409,616}{100\times 100}\:{m}^{2} \\\\\mapsto{\boxed{\mathfrak\green{Larger\:area = 440.9616 \:{m}^{2} }}}$