Question

A gift needs to be wrapped using wrapping paper. The dimensions of the gift are given in the following figure. Calculate the area of the wrapping paper required to cover the whole gift.

• A. $360\text{sq in}$
• B. $144\text{sq in}$
• C. $480\text{sq in}$
• D. $456\text{sq in}$

Answer 1

The correct option is C $480\text{sq in}$

The faces of the gift can be decomposed into $3$ rectangles and $2$ triangles.

First, we will calculate the area of the triangular faces.
Length of the triangular face $=12$ in
Height of the triangular face $=8$ in
Area of the triangle $=\frac{1}{2}\times$ length $\times$ height
$=\frac{1}{2}\times 12\times 8$
$=\frac{1}{2}\times 96$
$=48\text{sq in}$
Since there are $2$ triangular faces, the total area of the triangles $=$ 2 $\times$ area of one triangle
$=2\times 48=96\text{sq in}$
Now, we will calculate the area of the rectangular faces.
Length of the rectangular face $=12$ in
Width of the rectangular face $=10$ in
Area of the rectangle $=$ length $\times$ width
$=12\times 10$
$=120$ sq in
Since there are $2$ rectangular faces, the total area of the rectangles $=2\times$ area of one rectangle
$=2\times 120=240$ sq in
Since the face is a square, we will calculate the area of the square face.
Length of the square face $=12$ in
Area of the square $=$ length $\times$ length $=12\times 12$
$=144$ sq in
Since there is only one square face, here, the total area $=$ area of the square face $=144$ sq in
Total surface area of the wrapping paper required $=$ total area of the triangles $+$ total area of the rectangles $+$ total area of the square
$=96+240+144=480$ sq in