Question

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

Answer 1

Answer:

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Step-by-step explanation:

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.

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)

=》  ...(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 )

=》  ...(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

=》  

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

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• A cuboid has total surface area = 149 m²
• Lateral area = 135 m²

$\underline{\bf{Explanation\::}}$

As we know that formula of the total surface area of cuboid & lateral surface area;

• TSA of cuboid = 2(lb + bh + lh)
• Lateral area = 2h(l + b)

A/q

$\mapsto\tt{TSA = 2(lb+bh+lh) }$

$\mapsto\tt{2(lb+bh+lh) = 149 }$

$\mapsto\tt{2lb+2bh+2lh = 149............(1)}$

&

$\mapsto\tt{Lateral\:surface\:area = 135}$

$\mapsto\tt{2h(l+b) = 135}$

$\mapsto\tt{2lh + 2bh = 135..............(2)}$

Putting the value of 2lh + 2bh in equation (1),we get;

$\mapsto\tt{2lb + 135 = 149}$

$\mapsto\tt{2lb = 149 - 135}$

$\mapsto\tt{2lb = 14}$

$\mapsto\tt{lb = \cancel{14/2}}$

$\mapsto\tt{lb = 7\:m^2}$

Thus,

The area of it's base will be 7 m² .