Question

A flooring tile has a shape of rhombus whose diagonals are 8m and 3m. The number of such tiles required to cover a floor of area 1080 sq.m is:​

Answer 1

☯ Given,

• A flooring tile has a shape of rhombus whose diagonals are 8m and 3m.
• Area of floor is 1080 m².

☯ To Find,

• The number of such tile required.

☯ Solution,

Given, A flooring tile has a shape of rhombus whose diagonals are 8m and 3m.

⇒ Area of flooring tile = ¹/2 × 8 × 3

⇒ Area of flooring tile = 4 × 3

⇒ Area of flooring tile = 12 m²

Now,

Number of tiles = Area of floor/Area of flooring tile

⇒ Number of tiles = 1080/12

⇒ Number of tiles = 90

☯ Hence,

The number of such tile required is 90.

Answer 2

Given :-

• Length of the Diagonal 1 = 8m
• Length of the Diagonal 2 = 3m
• Area of the floor = 1080 m²

To find :-

• Number of tiles required to cover Floor. ..

Solution :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,3){1.5}}\put(0,0){\line(1,0){5}}\put(5,0){\line(1,3){1.5}}\put(1.5,4.5){\line(1,0){5}}\qbezier(1.56,4.5)(1.56,4.5)(5,0)\qbezier(6.45,4.5)(6.45,4.5)(0,0)\put(-0.5,-0.5){\sf}\put(1,4.8){\sf d1 (8 m )}\put(5.2,-0.5){\sf }\put(6.7,4.75){\sf d2 (3 m)}\put(3,1.6){\sf }\end{picture}$

Area of the tile is : (In the form of rhombus)

${\sf{\underline{\boxed{\bf{Area = \frac{1}{2} \times d_1 \times d_2 }}}}}$

${\sf{Area = \cfrac{1}{2} \times 8 \times 3}}$

${\sf{Area = 1\times 4 \times 3}}$

${ \underline{ \boxed{ \blue{\sf{Area = \: 12 \: {m}^{2} }}}}}$

So, Area of the Tile is 12m².

_________________________

Here, Number of tiles required is :-

${\sf{Number \: of \: tiles = \dfrac{Area\: of \: floor }{Area \: of \: tile}}}$

${\sf{Number \: of \: tiles = \dfrac{1080 \: {m}^{2} }{12 \: {m}^{2} }}}$

${\sf{Number \: of \: tiles = \dfrac{1080 \: }{12 \: }}}$

$\large{ \underline{ \boxed{ \red{\bf{Number \: of \: tiles = 90 \: tiles}}}}}$

So, required number of tiles is 90.