11. A cuboid has total surface area of 86 sq. m and its lateral surface area is 32 sq. m. Find the area of the base
Answers
Answer:
area of base L x B = 27
Step-by-step explanation:
solution------->
Given :-
total surface area of cuboid =86 sq.m
lateral surface area of cuboid=32 sq.m
now first we take
\begin{gathered}lateral \: surface \: area \: of \: cuboid = 2(l + b) \: h \\ \\ put \: the \: value \: we \: get\\ \\ 32 = 2(l + b)h \\ \\ \frac{32}{2} = (l + b)h \\ \\ (l + b)h = 16 \\ \\ now \: we \: can \: use \: \\ \\ total \: surface \: area \: of \: cuboid \: = 2(lh \: + bh \: + lb) \\ \\ 86 = 2(lh \: + bh \: + lb) \\ \\ \frac{83}{2} = (lh \: + bh \: + lb) \\ \\ now \: take \: common \\ \\ we \: get \\ \\ lb \: + h \: (b + l) = 43 \\ \\ now \: as \: per \: equation \: (1) \: we \: get \: h \: (l + b) = 16 \\ \\ lb \: + 16 = 43 \\ \\ lb \: = 43 - 16 \\ \\ lb \: = 27 \\ \\ \end{gathered}
lateralsurfaceareaofcuboid=2(l+b)h
putthevalueweget
32=2(l+b)h
2
32
=(l+b)h
(l+b)h=16
nowwecanuse
totalsurfaceareaofcuboid=2(lh+bh+lb)
86=2(lh+bh+lb)
2
83
=(lh+bh+lb)
nowtakecommon
weget
lb+h(b+l)=43
nowasperequation(1)wegeth(l+b)=16
lb+16=43
lb=43−16
lb=27
area of the base = 27
Step-by-step explanation: