A cuboid has a total surface area of 149sq.m and its lateral surface area is 135sq.m. Find the area of its base.
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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.
Step-by-step explanation:
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