Question

a flooring tile has the shape of a parallelogram whose base is 24cm and the corresponding height is 10cm. How much tile are required to cover a floor area 1080m square? if required you can spit tiles in whatever you want to fill up the corners. ​

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Areas of Parallelogram has been used. We are already given the area of floor. Then first we need to convert that area into standard unit of cm². Then we will find the area of each tile. To fibs number of tiles we will divide the area of floor by area of each tile. This is because sum of areas covered by all the tiles will be equal to the area of floor.

Let's do it !!

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★ Equations Used :-

$\\\;\boxed{\sf{1\;m^{2}\;=\;\bf{10000\;cm^{2}}}}$

$\\\;\boxed{\sf{Area\;of\;Parallelogram\;=\;\bf{Base\;\times\;Height}}}$

$\\\;\boxed{\sf{Number\;of\;Tiles\;=\;\bf{\dfrac{Area\;of\;Floor_{(in\;cm^{2})}}{Area\;of\;Each\;Tile}}}}$

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★ Solution :-

Given,

» Base of each Tile = 24 cm

» Height of each Tile = 10 cm

» Area of the Floor = 1080 m²

Note :- Area of each tiles is equal.

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~ For the Area of Floor in cm² :-

We know that,

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;1\;m\;=\;\bf{100\;cm}}$

Now squaring both the sides, we get,

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;(1\;m)^{2}\;=\;\bf{(100\;cm)^{2}}}$

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;1\;m^{2}\;=\;\bf{10000\;cm^{2}}}$

Now, 1080 m² will be given as :-

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;1080\;m^{2}\;=\;\bf{1080\;\times\;10000\;cm^{2}}}$

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;1080\;m^{2}\;=\;\bf{10800000\;cm^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Floor\;\;=\;\bf{10800000\;\;cm^{2}}}}}$

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~ For the Area of Each Tile :-

$\\\;\;\;\;\;\sf{:\Rightarrow\;\;\;Area\;of\;Parallelogram_{(Tile)}\;=\;\bf{Base\;\times\;Height}}$

$\\\;\;\;\;\;\sf{:\Rightarrow\;\;\;Area\;of\;Parallelogram_{(Tile)}\;=\;\bf{24\;\times\;10}}$

$\\\;\;\;\;\;\sf{:\Rightarrow\;\;\;Area\;of\;Parallelogram_{(Tile)}\;=\;\bf{240\;\;cm^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Each\;\;Tile\;\;=\;\bf{240\;\;cm^{2}}}}}$

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~ For the Number of Tiles Required :-

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;Number\;of\;Tiles\;=\;\bf{\dfrac{Area\;of\;Floor_{(in\;cm^{2})}}{Area\;of\;Each\;Tile}}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;Number\;of\;Tiles\;=\;\bf{\dfrac{10800000}{240}}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;Number\;of\;Tiles\;=\;\bf{45000}}$

This means that there is no need of splitting any tile to cover corners.

$\\\;\large{\underline{\underline{\rm{Thus,\;number\;of\;Tiles\;required\;to\;cover\;floor\;are\;\;\boxed{\bf{45000\;\;Tiles}}}}}}$

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★ More Formulas to Know :-

$\\\;\tt{\leadsto\;\;\;Area\;\;of\;\;Rectangle\;\;=\;Length\;\;\times\;\;Breadth}$

$\\\;\tt{\leadsto\;\;\;Area\;\;of\;\;Square\;\;=\;\;(Side)^{2}}$

$\\\;\tt{\leadsto\;\;\;Area\;\;of\;\;Circle\;\;=\;\;\pi r^{2}}$

$\\\;\tt{\leadsto\;\;\;Area\;\;of\;\;Triangle\;\;=\;\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\tt{\leadsto\;\;\;Area\;\;of\;\;Triangle_{(Alternative)}\;\;=\;\;\sqrt{s(s\;-\;a)(s\;-\;b)(s\;-\;c)}}$

$\\\;\tt{\leadsto\;\;\;Semi\:-\:perimeter\;\;of\;\;\Delta\;=\;\dfrac{Sum\;\;of\;\;all\;\;sides,\;a\;+\;b\;c}{2}}$

Answer 2

$\large{\boxed{\boxed{\sf{Question}}}}$

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How much tile are required to cover a floor area 1080 m² ? If required you can spit tiles in whatever you want to fill up the corners.

$\: \: \: \large{\boxed{\boxed{\sf{Answer}}}}$

$\sf Given \; that \begin{cases} & \sf{Paralloegram \: is \: given} \\ & \sf{Base \: of \: paralloegram = \bf{24 \: cm}} \\ & \sf{Height \: of \: paralloegram = \bf{10 \: cm}} \\ & \sf{Area \: of \: floor = \bf{1080m^{2}}} \end{cases}$

$\sf To \: find \begin{cases} & \sf{How \: much \: tiles \: are \: required} \end{cases}$

$\sf Solution \begin{cases} & \sf{45000 \: tiles \: are \: required} \end{cases}$

$\sf Also \: says \: that \begin{cases} & \sf{If \: required \: we \: can \: spit \: tiles \: in \: whatever \: we \: want \: to \: fill \: up \: the \: corners} \end{cases}$

$\large{\boxed{\boxed{\underbrace{\sf{Understanding \: the \: concept \: 1st}}}}}$

This question says that there are flooring tiles in a shape of paralloegram. Afterwards it says that the corresponding base and corresponding height are 24 and 10 cm respectively. Afterwards it says that we have to find the numbers of tiles to cover a floor and the area of floor is 1080 m². (Wow) As we see that the height nd base are given in cm and the area is given in m². So, we have to convert any one of them into its opposite. So, we covert m² into cm² because it's easy to convert. Afterwards the questy says that if required then we can spit tiles in whatever we want to fill up the corners !

$\large{\boxed{\boxed{\underbrace{\sf{Some \: procedure}}}}}$

To solve this question we have to see and use the concepts and the formulas. 1st seeming what is given or what to find. Afterwards finding the area of tiles by using the formula to find the area of paralloegram we use it coz tiles are in a shape of paralloegram. Afterwards converting m² into cm² we have to multiply the area of oor by it. Afterwards finding the number of tiles we have to use the formula to find A of floor / A of tiles (each) afterthat putting the values we get our final result that is 45000 tiles.

$\large{\boxed{\boxed{\underbrace{\sf{We \: also \: write \: these \: as}}}}}$

☀ Area as A.

☀ Base as B

☀ Height as H.

☀ square as ²

☀ Centimetres as cm

☀ Metres as m

$\large{\boxed{\boxed{\underbrace{\sf{Using \: concepts}}}}}$

☀ Area of paralloegram.

☀ Converting m² into cm²

☀ Number of tiles

$\large{\boxed{\boxed{\underbrace{\sf{Using \: formulas \: according \: to \: concepts}}}}}$

☀ Area of paralloegram = Base × Height

☀ 1m² = 10000 cm²

☀ Number of tiles = Area of floor / Area of each tiles.

$\large{\boxed{\boxed{\underbrace{\sf{Full \: solution}}}}}$

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• Base of tiles = 24 cm (Given)

• Height of tiles = 10 cm (Given)

• Area of floor = 1080 m² (Given)

• Number of tiles (To find)

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Now finding the area of tiles (each)

Area of paralloegram = B × H

Area of paralloegram = 24 × 10

Area of paralloegram = 240 cm²

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Now finding the area of floor in cm²

As we know that,

1 metre = 100 cm

But here m² is given so,

1 m² = 10,000 cm²

Now according to this question,

1080 m² = 10,000 × 1080

1080 m² = 1,08,00,000 cm²

Hence, area of floor = 1,08,00,000 cm²

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Now, finding number of tiles

Number of tiles = A of floor / A of each tile.

Number of tiles = 1,08,00,000 / 240

Number of tiles = 10,80,000 / 24

Number of tiles = 540000 / 12

Number of tiles = 270000 / 6

Number of tiles = 135000 / 3

Number of tiles = 45000

This means that there is no requirement to us to can spit tiles in whatever we want to fill up the corners.

Hence, tiles = 45000.

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