Question

4. A flooring tile has the shape of a parallelogram whose base is 24 cm and the
corresponding height is 10 cm. How many such tiles are required to cover a floor of
area 1080 m²? (If required you can split the tiles in whatever way you want to fill up
the corners).​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 4. \:A \:flooring\: tile\: has\: the\: shape\: of\: a \:parallelogram\\\tt whose\: base\: is \:24 \:cm\: and\: the \:corresponding \:height\\\tt is\: 10 \:cm.\: How\: many \:such\: tiles\: are\: required\\\tt to\: cover\: a \:floor\: of\: area\: 1080\: {m}^{2}?\\\tt (If\: required\: you\: can \:split\: the\: tiles\: in\\\tt whatever\: way \:you\: want \:to \:fill up\: the\: corners).$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf Base\:of \:the \: parallelogram =24\:cm$
• $\sf \bf Height\:of \:the \: parallelogram =10\:cm$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf (i) \:Area\:of \:1\:tile$
• $\sf \bf (ii) \:Number \:of\:tiles\:required \:to \:cover \:the \:floor$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\color {lightgreen} \underline {\sf Converting \:m\:to\:cm}}$

${\boxed{\color {blue} {\bf {\Big(1\:m\Big)}^{2}={\Big(100\:cm\Big)}^{2}}}}$

$\sf \bf \implies 1080\:{m}^{2}=1080 \times {\Big(100\Big)}^{2}$

$\sf \bf \implies 1080\:{m}^{2}=1080 \times 10000$

$\implies {\boxed {\boxed {\color {green} {\sf \bf 1080\:{m}^{2}=10800000\:{cm}^{2}}}}}$

——————————————————————————

${\color {lightgreen} {\underbrace {\sf \bf (i) \:Area\:of \:1\:tile}}}$

${\color {gold} \underline {\sf Let \:the \:area \:of \:tile\:in\:the\:shape \:of \:a \: parallelogram \:be\:x}}$

${\boxed{\boxed {\boxed{\boxed {\color {blue} {\sf \bf A=b\times h}}}}}}$

• $\sf A=area \:of \: parallelogram$
• $\sf b=base \:of\:the \: parallelogram$
• $\sf h=height \:of\:the \: parallelogram$

${\underbrace {\overbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies x=24\times 10$

$\implies {\boxed{\boxed {\color {green} {\sf \bf x=240\:{cm}^{2}}}}}$

${\color {purple} \underline {\tt \therefore Area\:of \:1\:tile \:is\:240\:{cm}^{2}}}$

——————————————————————————

${\color {lightgreen} {\underbrace {\sf \bf (ii) \:Number \:of\:tiles\:required \:to \:cover \:the \:floor}}}$

${\boxed {\boxed {\boxed{\color {blue} {\sf \bf Number \:of \:tiles\:required =\dfrac{Area\:of \:floor}{Area\:of \:1\:tile}}}}}}$

${\color {gold} \underline {\sf Let \:the\: Number \:of \:tiles\:required \:be\:y}}$

${\underbrace {\overbrace {\color {orange} {\bf Substitute \:the \:values}}}}$

$\sf \bf \implies y=\dfrac{10800000}{240}$

$\sf \bf\implies y=\dfrac{\cancel {10800000}}{\cancel {240}}$

$\implies {\boxed {\boxed {\color {yellow} {\sf \bf y=45000}}}}$

${\underbrace {\color {red} \underline {\sf \therefore 45000 \:tiles\:are\:required \:for \:covering \:the \:floor}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\bf Area \:of\: triangle = \dfrac{1}{2}b h$

$\bf Area \:of\: parallelogram = b\times h$

$\bf Area \:of \:rectangle= l\times b$

$\bf Area \:of \:square = {a}^{2}$