Question

The floor of a room is rectangularin shape. Its length is 8 m and breadth 7 m. Heightof the room is Its 4 m. Find the are a of the four walls of the room : (A) 180 m2 C) 120 m2 (B) 130 m2 (D) 150 m2​

Answer 1

Given :

• Dimensions of floor = 8 m × 7 m
• Height of the room = 4 m

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To Find :

• Find the Area of four walls .

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Solution :

~ Formula Used :

• Total Surface Area :

${\purple{\dashrightarrow}} \: \: {\underline{\overline{\boxed{\red{\pmb{\sf{ LSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}}}$

• Area :

${\purple{\dashrightarrow}} \: \: {\underline{\overline{\boxed{\red{\pmb{\sf{ Area{\small_{(Rectangle)}} = L \times B }}}}}}}$

Where :

• ➳ TSA = Total Surface Area
• ➳ L = Length
• ➳ B = Breadth
• ➳ H = Height
• ➳ A = Area

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~ Calculating the TSA of Room :

${\longmapsto{\qquad{\sf{ TSA{\small_{(Room)}} = 2(lb + bh + hl) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA{\small_{(Room)}} = 2[( 8 \times 7) + (7 \times 4) + (4 \times 8)] }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA{\small_{(Room)}} = 2( 56 + 28 + 32) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA{\small_{(Room)}} = 2 \times 116 }}}} \\ \\ \ {\qquad{\textsf{ Lateral Surface Area of the Room = {\pink{\sf{ 232 \: m² }}}}}}$

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~ Calculating the Area of Top and Bottom :

• Area of Top :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Top)}} = L \times B }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Top)}} = 8 \times 7 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Top of the Room = {\green{\sf{ 56 \: m² }}}}}}$

• Area of Bottom :

${\longrightarrow{\qquad{\sf{ Area{\small_{(Bottom)}} = L \times B }}}} \\ \\ \ {\longrightarrow{\qquad{\sf{ Area{\small_{(Bottom)}} = 8 \times 7 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Bottom of the Room = {\green{\sf{ 56 \: m² }}}}}}$

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~ Calculating the Area of 4 walls :

${\dashrightarrow{\qquad{\sf{ Area{\small_{(4 \: walls)}} = TSA{\small_{(Room)}} - Area{\small_{(Top)}} - Area{\small_{(Bottom)}} }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area{\small_{(4 \: walls)}} = 232 \: m² - 56 \: m² - 56 \: m² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area{\small_{(4 \: walls)}} = 232 \: m² - 56 \: m² - 56 \: m² }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area{\small_{(4 \: walls)}} = 176 \: m² - 56 \: m² }}}} \\ \\ \ {\qquad{\textsf{ Area of the 4 walls = {\orange{\sf{ 120 \: m² }}}}}}$

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Therefore :

❝ (c.) option is correct . ❞

$\\ {\red{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}{\pink{\underline{\rule{75pt}{9pt}}}}$

Answer 2

★ Given:-      

• ➝ Length of the room = 8m
• ➝ Breadth of the room = 7m
• ➝ Height of the room = 4m

★ To find:-    

• ➝ The area of the four walls of the room

★ Solution:-    

Here, we have given that the floor of a room is rectangular in shape. its length is 8 m, breadth 7 m and the height of the room is 4 m. And we have to find out the area of the four walls of the room.

So, to find out the area of the room's four walls. we, will use the formula and substitute the values.

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〈〈 Area of the four walls 〉〉

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:}$

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:2h\:(\:l\:+\:b\:)}$

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:2\:\times\:4\:(\:8\:+\:7\:)}$

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:2\:\times\:4\:(\:15\:)}$

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:8\:(\:15\:)}$

$\qquad\tt{:\implies\:Area\:of\:the\:4\:walls\:_{(\:ROOM\:)}\:=\:120\:m^{2}}$

So, Option c) 120 m² is the correct answer.

. ° . The area of the four walls of the room is 120 m².

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