Question

A cuboid has a total surface area of 100 m2 and the lateral surface area is 50 m². Find the area of
its base.
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Answer 1

Answer:

he total surface area of cuboid = 2(lb+bh+hl)=100m²

lateral surface area of cuboid=2h(l+b)=50m²

so TSA =2h(l+b) + 2lb

so 100m²=50+2lb

50/2=lb

25m² is the area of base

Step-by-step explanation:

Answer 2

Correct Question:-

A cuboid has a total surface area of 100 m² and the lateral surface area is 50 m². Find the area of its base.

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Answer:-

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Given:

▪︎T.S.A. of cuboid = 100m²

▪︎L.S.A. of cuboid = 50m²

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To Find:

▪︎Area of base

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Solution:

According to given conditions;

T.S.A. - L.S.A. = 100 - 50 m²

= 2(lb+bh+hl) - 2(l+b)h = 50m²

= $2lb + \cancel{2bh} + \cancel{2hl} - \cancel{2lb} - \cancel{2bh}$ = 50m²

= 2lb = 50m²

= lb = 50 ÷ 2

= lb = 25m²-----eq.①

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As we know,

Area of base

= length × breadh

By putting equation ①

lb = 25m²

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Formula to be remembered:-

▪︎T.S.A. of cuboid = 2(lb+bh+hl)

▪︎C.S.A. of cuboid = 2(l+b) × h

▪︎Volume of cuboid = l × b × h