Question

Q3. 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? [lf required you can split the tiles in whatever way you want to
fill up the corners]

Answer 1

$\huge\bold{\underbrace{Answer}}$

Given :

• Base of parallelogram is 24 cm
• Corresponding height of parallelogram if 10 cm

To fine :

• Tiles required to cover a floor of area of 1080 m²

Formula used :

• Area of parallelogram = Base * Height

Solution :

${\implies}$ Firstly let's find out the area of parallelogram.

Area of parallelogram = Base * Height

Base = 24 cm

Height = 10 cm

${\implies}$Area of parallelogram = 24cm * 10cm = 240 cm

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${\implies}$ Secondly, let's find out the area of floor in centimetre.

Area of floor = 1080 m²

So here, we should convert metre into centimetre.

1 m = 100 cm

1 m² = 100 cm²

${\implies}$ Area of floor = 1080 * 100²= 10800000 cm

_____________

${\implies}$ Lastly, let's find out the number of tiles required to cover a floor of area 1080 m².

${\implies}$ Number of tiles = $\bf\dfrac{Area \ of \ floor}{Area \ of \ paralellogram}$

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

${\implies}$ = 45000

_____________

Hence, 45000 tiles are required to cover a floor of 1080m².

Answer 2

Answer :-

$\: \\ \large{\underline{\underline{\sf{Firstly,\;let's\;understand\;the\;Concept\;Used\;:-}}}}$

Here the concept of Areas of Parallelogram has been used. We are given the dimensions of Parallelogram. By using that we can find its area. Then, we are also given the area of floor that is to be tiled. We can divide the area of floor by the area of each tile to find out number of tiles. Because area of that number of tile will be equal to area of floor and the dimensions of each tile are equal.

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★ Formula Used :-

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

$\: \\ \large{\boxed{\sf{Number\;of\;tiles\;\;=\;\;\bf{\dfrac{Area\;of\;Floor_{(in\;cm^{2})}}{Area\;of\;each\;Tile_{(in\;cm^{2})}}}}}}$

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

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★ Question :-

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?

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★ Solution :-

Given,

» Base of each tile = 24 cm

» Height of each tile = 10 cm

» Area of floor = 1080 m²

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~ For area of Floor (in m²) :-

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

$\: \\ \large{\sf{:\rightarrow\;\;\; 1080\;\;m^{2} \;\; = \;\; \bf{1080 \:\times\:10000\;\; cm^{2} \: \: = \: \: \underline{\underline{10800000 \;\;cm^{2}}}}}}$

$\: \\ \large{\boxed{\boxed{\sf{Area\;of\;Floor\;\; = \; \bf{10800000\;\;cm^{2}}}}}}$

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~ For Area of Each Tile :-

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

$\: \\ \qquad \large{\sf{:\longrightarrow\:\;\;Area\;of\;Parallelogram_{(Tile)}\;\;=\;\;\bf{24\:\times\:10 \;\; = \; \; \underline{\underline{240\;\;cm^{2}}}}}}$

$\: \\ \large{\boxed{\boxed{\sf{Area\;of\;Each\;Tile\;\: = \; \bf{240\;\;cm^{2}}}}}}$

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~ For the number of tiles required :-

$\: \\ \qquad \large{\sf{:\Longrightarrow\;\;\:Number\;of\;tiles\;\;=\;\;\bf{\dfrac{Area\;of\;Floor_{(in\;cm^{2})}}{Area\;of\;each\;Tile_{(in\;cm^{2})}}}}}$

$\: \\ \qquad \large{\sf{:\Longrightarrow\;\;\:Number\;of\;tiles\;\;=\;\;\bf{\dfrac{10800000}{240} \: \: = \: \: \underline{\underline{45000}}}}}$

$\: \\ \large{\underline{\underline{\rm{Thus,\;number\;of\;tiles\;required\;are\;\;\boxed{\bf{45000}}}}}}$

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★ More to know :-

• Area of Square = (Side)²

• Area of Rectangle = Length × Breadth

• Area of Triangle = ½ × Base × Height

• Area of Circle = πr²

• Area of Semicircle = ½ × πr²