Question

A cuboid has a total surface area of 149 sq.Units and its lateral surface area is 135 sq.Units.Find the area of the base

Answer 1

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

A cuboid has total surface area of 149 sq. units and it's lateral surface area is 135 sq. units . Find the area of the base.

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

Total surface area of the cuboid = 149 sq. units

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

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

=》 149 = 2 ( lb + bh + lh)

=》 $\tt{lb + bh + lh = 74.5}$ ...(1)

Lateral surface area of the cuboid = 135 sq. m

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

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

=》 135 = 2 ( lh + bh )

=》 $\tt{lh + bh = 67.5}$ ...(2)

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

=》 lb + bh + lh = 74.5

We know that :-

lh + bh = 67.5

=》 lb + 67.5 = 74.5

=》 lb = 74.5 - 67.5

=》 $\tt{lb = 7 unit^{2}}$

Thus, the area of the base is equal to 7 sq. units.

Answer 2

Step-by-step explanation:

Total surface area of the cuboid = 149 sq. units

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

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

=》 149 = 2 ( lb + bh + lh)

=》 \tt{lb + bh + lh = 74.5}lb+bh+lh=74.5 ...(1)

Lateral surface area of the cuboid = 135 sq. m

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

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

=》 135 = 2 ( lh + bh )

=》 \tt{lh + bh = 67.5}lh+bh=67.5 ...(2)

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

=》 lb + bh + lh = 74.5

We know that :-

lh + bh = 67.5

=》 lb + 67.5 = 74.5

=》 lb = 74.5 - 67.5

=》 \tt{lb = 7 unit^{2}}lb=7unit

2

Thus, the area of the base is equal to 7 sq. units.