Question

A cuboid has total surface area of 86 square m and its lateral surface area is 32 square metre find the area of the base

Answer 1

$\underline{\mathfrak{\huge{The\:Question:}}}$

A cuboid has total surface area of 86 sq. m and it's lateral surface area is 32 sq. m . Find the area of the base.

$\underline{\mathfrak{\huge{Your\:Answer:}}}$

Total surface area of the cuboid = 86 sq. m

Total surface area of a cuboid = 2 ( lb + bh + lh )

Keep them equal and then find the value of the variables :-

=》 86 = 2 ( lb + bh + lh)

=》 $\tt{lb + bh + lh = 43}$ ...(1)

Lateral surface area of the cuboid = 32 sq. m

Lateral surface area of a cuboid = 2 ( lh + bh )

Keep them equal and then solve and find the values of the variables:-

=》 32 = 2 ( lh + bh )

=》 $\tt{lh + bh = 16}$ ...(2)

Put the value of (2) in (1) and then find the value of the let over variable :-

=》 lb + bh + lh = 43

We know that :-

lh + bh = 16

=》 lb + 16 = 43

=》 lb = 43 - 16

=》 $\tt{lb = 27 m^{2}}$

Thus, the area of the base is equal to 27 sq. m.