Question

Which of the following is correct for a rectangular prism?

• A. Total surface area of a rectangular prism $>$ Lateral surface area of a rectangular prism
• B. Total surface area of a rectangular prism $<$ Lateral surface area of a rectangular prism
• C. Total surface area of a rectangular prism $=$ Lateral surface area of a rectangular prism
• D. None of these

Answer 1

The correct option is A Total surface area of a rectangular prism $>$ Lateral surface area of a rectangular prism

Let,
Length of the rectangular prism $=l$

Breadth of the rectangular prism $=b$

Height of the rectangular prism $=h$

$\to$The lateral surface area of a rectangular prism = 2( l + b) h

$\to$The total surface area of a rectangular prism $=2\left(lb\right)+2\left(bh\right)+2\left(lh\right)$

$=2\left(lb\right)+2(l+b)h$

Total surface area of a rectangular prism $=2lb+$ lateral surface area of a rectangular prism

Hence, Total surface area of a rectangular prism $>$ lateral surface area of a rectangular prism

$\to$The lateral surface area of a rectangular prism is $2(l+b)h$.