Question

A square pyramid was placed on top of a rectangular prism to make a dollhouse. The dimensions of the dollhouse are given below. Robin wants to decorate her dollhouse with stickers of $1$ square inch each. Calculate the number of stickers required to cover all outer faces of the dollhouse.

• A. $1084\text{sq in}$
• B. $1728\text{sq in}$
• C. $2484\text{sq in}$
• D. $2084\text{sq in}$

Answer 1

The correct option is C $2484\text{sq in}$

To make a dollhouse, we will combine the two given diagrams.

If Robin wants to decorate it from the outside, then we need to find the area of all the faces.
Number of triangles $=4$
Number of rectangles $=4$
Number of squares $=1$

First, we will calculate the area of the triangular faces.
Length of the triangular face $=18in$
Height of the triangular face $=12in$
Area of the triangle $=\frac{1}{2}\times$ length $\times$ height
$=\frac{1}{2}\times 18\times 12$
$=\frac{1}{2}\times 216$
$=108\text{sq in}$
Since there are 4 triangular faces, the total area of the triangles = 4 $\times$ area of one triangle $=4\times 108=432$ sq in
Now, we will calculate the area of the rectangular faces.
Length of the rectangular face $=24$ in
Width of the rectangular face $=18$ in
Area of the rectangle $=$ length $\times$ width
$=24\times 18$
$=432$ sq in
Since there are $4$ rectangular faces, the total area of the rectangles = 4 $\times$ area of one rectangle $=4\times 432=1728$ sq in
Now, we will calculate the area of the square face.
Length of the square face $=18$ in
Area of the square $=$ length $\times$ length
$=18\times 18$
$=324$ sq in
Since there is 1 square face, here, the total area $=1\times$ area of the square $=1\times 324=324$ sq in
Total surface area of the stickers required to cover the doll house $=$ total area of the triangles + total area of the rectangles $+$ total area of the square
$=432+1728+324=2484\text{sq in}$.