Question

A cuboid has a total surface area of 65m² and lateral surface area is 37m² . Find out the area of the base. ​

Answer 1

Lateral surface area of a cuboid =2(b×h+l×h)

Total surface area of a cuboid =2(l×b+b×h+l×h)

=2(l×b)+2(b×h+l×h)

=2× Area of the base + Lateral surface area

Hence, 40=2× Area of the base +26

=>2× Area of the base =14

Area of the base =7m

2

Answer 2

$\frak{Given}\begin{cases}\sf{\;\;\; TSA_{(Total \; surface\; area)} = 65\;m^2}\\\sf{\;\;\; LSA_{(Lateral\; surface\; area)} = 37\;m^2}\end{cases}$

Need to find: Area of the base.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀

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$\star\;\boxed{\sf{\pink{LSA_{\:(cuboid)} = 2h(l + b)}}}$

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where,

• h is height of cuboid, l is length of cuboid and b is breadth of the cuboid, respectively.

Therefore,

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$:\implies\sf LSA = 2(l + b)h = 37 \\\\\\:\implies\sf 2lh + 2bh = 37\qquad\quad\bigg\lgroup\bf Equation (I)\bigg\rgroup$

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Similarly,

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$\star\;\boxed{\sf{\purple{TSA_{\:(cuboid)} = 2(lb + bh + hl)}}}$

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$:\implies\sf TSA = 2(lb + bh + hl) = 65 \\\\\\:\implies\sf 2lb + 2bh + 2hl = 65\\\\\\:\implies\sf 2lb + 37 = 65\\\\\\:\implies\sf 2lb = 65 - 37\qquad\quad\bigg\lgroup\bf From\;Equation (I)\bigg\rgroup \\\\\\:\implies\sf 2lb = 28\\\\\\:\implies\sf lb = \cancel\dfrac{28}{2}\\\\\\:\implies{\underline{\boxed{\sf{\purple{lb = 14\;m^2}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\;area\; of \; Base \; of \; cuboid\; is \:\bf{14\;m^2 }.}}}$

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$\qquad\boxed{\bf{\mid{\overline{\underline{\red{\bigstar\: Formulas\:related\:to\:cuboid:}}}}}\mid}$

• $\sf Base\: Area\: of\: cuboid = \bf{l \times b}$

• $\sf Total\:surface\:area\:of\: cuboid = \bf{2(lb + bh + hl)}$

• $\sf Curved\:surface\:area\:of\: cuboid = \bf{2(l + b) \times h}$

• $\sf Volume\:of\:cuboid = \bf{l \times b \times h}$