Question

A toy is in the shape of a pyramid mounted on the top of a square prism as shown. What will be the minimum area of the wrapping material needed to cover the toy completely?

• A. $316$ sq in
• B. $420$ sq in
• C. $352$ sq in
• D. $416$ sq in

Answer 1

The correct option is D $416$ sq in

The base length of the pyramid $=8$ in
The slant height of the pyramid $=6$ in

Total surface area = Surface area of the base of the prism + Surface area of the 4 faces of the prism + Surface area of the 4 triangular faces of the pyramid
$=8\times 8+4\times (8\times 8)+4\times (\frac{1}{2}\times 8\times 6)$
$=5\times (8\times 8)+4\times (4\times 6)$
$=5\times 64+4\times 4\times 6$
$=320+96$
$=416$ sq in

The minimum area of the wrapping material needed to cover the toy completely is $416$ sq in.