Question

A cuboid has total surface area of 40m2 and it's lateral surface area is 26m.find the area of its base

Answer 1

$\huge\mathbb{SOLUTION:-}$

• Given that the surface area of cuboid is 40 square metre
• L.S. A=26 square metre

$\bf\underline{\underline{According\:To\: Question:-}}$

$\boxed{\sf{T.S.A=2(lb+bh+lh)}}$

$\boxed{\sf{L.S.A=2(l+b)h}}$

• or L.S.A=2(bh+lh)

$\sf\implies 40=26+2lb\\ \\ \sf\implies 40-26=2lb\\ \\ \sf\implies 14=2lb\\ \\ \sf\implies \cancel{\frac{14}{2}}=lb\\ \\ \sf\implies 7m{}^{2}=lb$

$\boxed{\sf{Area\:of\:base=7m{}^{2}}}$

Answer 2

Answer:

$\small\red{\boxed{\bold{Area \:of \:base\:=7m^2}}}$

$\tt{Given}\begin{cases}\tt{40 \:square \:meter } \\ \tt{lateral\: surface\: area =26}\end{cases}$

$\huge\underline\textsf{Explantion:- }$

$\small\underline\textsf{formula \:used }$

$\implies\bf t.s.a = 2(lb + bh + lh)$

$\implies\bf l.s.a = 2(l + b)h$

$\rule{300}{2}$

$\implies\bf l.s.a = 2(bh + 2lb)$

$\implies\bf40 = 26 + 2lb$

$\implies\bf40 - 26 = 2lb$

$\implies\bf14 = 2lb$

$\implies\bf \frac{\cancel{14}}{ \cancel2} = lb$

$\implies\bf7m {}^{2}$