Question

Find the total surface of the room whose dimensions are 14m 10m and 5m

Answer 1

Answer:-

• The total surface area of the room is 520m²

Step-by-step explanation:

$\frak {Given} = \begin{cases} &\sf{Lenght\:of\:the\:room\:=\:14m} \\\\ &\sf{Breadth\:of\:the\:room\:=\:10m} \\\\ &\sf{Height\:of\:the\:room\:=\:5m}\end{cases}$

$\frak {To\:find\:=\:Total\:surface\:area\:of\:the\:room\:}$

$\boxed{\underline{\texttt{Solution :-}}}$

• Here we have the length, breadth and height of the room so it is of cuboidal shape, hence we will use the formula of the total surface area of the cuboid.

$\sf{Total\:surface\:area\:of\:the\:room\:=\:Total\:surface\:area\:of\:the\:couboid}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2(\:Lb\:+\:bh\:+\:hL)}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2(\:14\:\times\:10\:+\:10\:\times\:5\:+\:5\:\times\:14\:)}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2(\:140\:+\:50\:+\:70\:)}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2(\:260\:)}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2\:\times\:260}$

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:520m}$

• Hence the total surface area of the room is 520m²

_______________________

$\longmapsto\sf{Total\:surface\:area\:of\:the\:room\:=\:2(\:Lb\:+\:bh\:+\:hL)}$

Where

• L = length
• b = breadth
• h = height

Answer 2

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given\::- }}}}$

• Length of rectangle = 14 m

• Breadth of rectangle = 10 m

• Area of rectangle = 5 m

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To\:find\::- }}}}$

• Total surface area of room.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Formula\::- }}}}$

$\large\sf\red{ Total\:surface\: area\:of\: rectangle = 2(lb+bh+hl)}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution\::- }}}}$

$\dashrightarrow\qquad\sf Length \: of \: rectangle = 14\:m$

$\dashrightarrow\qquad\sf Breadth\: of \:rectangle = 10\:m$

$\dashrightarrow\qquad\sf Height\: of \:rectangle = 5\:m$

$\dashrightarrow\qquad\sf Total\:surface\:area\:of \:rectangle = 2(lb+ bh+ hl)$

$\dashrightarrow\qquad\sf = 2(14 \times 10+ 10 \times 5+ 5 \times 14)$

$\dashrightarrow\qquad\sf = 2(140 + 50 + 70 )$

$\dashrightarrow\qquad\sf = 2 \times 260$

$\dashrightarrow\qquad\sf = 520m^2$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Therefore, }}}}$

$\large\sf\red{ Total\:surface\: area\:of\: room = 520m^2}$