Question

A hall is 16 metres long 14 metres broad and 10 m. high. Each wall has a door 5 metres long and 4 metres wide and a window 3 metres long and 2 metres wide. Find the area of the four walls of the room.​

Answer 1

Given :

• Dimensions of a hall is 16 m × 14 m × 10 m .
• Each wall has a door 5 m × 4 m and a window of dimensions 3 m × 2 m.

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To Find :

• Find the Area of 4 walls of the room .

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Solution :

~ Concept :

We can apply the concept of Lateral Surface Area here and calculate the Area of whole room .Than, we will subtract area of Top and the bottom from the Lateral Surface Area we will get the Area of 4 walls . subtract area of door and window from the Area of 4 walls .Finally, we will get the Area of walls without walls and windows . Let's Solve :

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~ Formula Used :

$\large{\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\sf{ LSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}}}$

$\large{\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\sf{ Area{\small_{(Rectangle)}} =Length \times Breadth }}}}}}}$

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~ Calculating the Surface Area of Room :

${\longmapsto{\qquad{\sf{ LSA{\small_{(Room)}} = 2(lb + bh + hl) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ LSA{\small_{(Room)}} = 2[( 16 \times 14 ) + (14 \times 10) + (10 \times 16)] }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ LSA{\small_{(Room)}} = 2(224 + 140 + 160) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ LSA{\small_{(Room)}} = 2 \times 524 }}}} \\ \\ \ {\qquad{\textsf{ Surface Arra of the Room = {\color{darkblue}{\sf{ 1048 \: m² }}}}}}$

~ Calculating the Area of Top and Botton Surface :

• Top Surface :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Top \: Surface)}} = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Top \: Surface)}} = 16 \times 14 }}}} \\ \\ \ {\qquad{\textsf{ Area of Top Surface = {\color{maroon}{\sf{ 224 \: m² }}}}}}$

• Bottom Surface :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Bottom \: Surface)}} = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Bottom \: Surface)}} = 16 \times 14 }}}} \\ \\ \ {\qquad{\textsf{ Area of Bottom Surface = {\color{maroon}{\sf{ 224 \: m² }}}}}}$

~ Calculating the Area of 4 walls :

${\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls )}} = LSA{\small_{(Room)}} - Area{\small_{(Top)}} - Area{\small_{(Bottom)}} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls)}} = 1048 - 224 - 224 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls)}} = 824 - 224 }}}} \\ \\ \ {\qquad{\textsf{ Area of the 4 walls = {\orange{\sf{ 600 \: m² }}}}}}$

~ Calculating the Area of Doors and Windows :

• Area of Door :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Door)}} = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Door)}} = 5 \times 4}}}} \\ \\ \ {\qquad{\textsf{ Area of the Door = {\color{maroon}{\sf{ 20 \: m² }}}}}}$

• Area of Window :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Windows)}} = Length \times Breadth }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Windows)}} = 3 \times 2}}}} \\ \\ \ {\qquad{\textsf{ Area of the Window = {\color{maroon}{\sf{ 6 \: m² }}}}}}$

~ Calculating Area of 4 walls (without doors and Windows) :

${\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls )}} = Area{\small_{(4 \: walls)}} - Area{\small_{(Door)}} \times 4 - Area{\small_{(Window)}} \times 4 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls )}} = 600 - (20 \times 4) - (6 \times 4) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls )}} = 600 - 80 - 24 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area{\small_{(4 \: Walls )}} = 520 - 24 }}}} \\ \\ \ {\qquad{\textsf{ Area of the 4 walls = {\red{\sf{ 496 \: m² }}}}}}$

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~ Therefore :

❝ Area of the walls is 496 m² . ❞

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