AbeNeedsAnswers wrote: ↑Sun May 05, 2019 9:24 pm
A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?
Each side of each triangular piece of tile is 9 centimeters long.
The mosaic can be put inside a rectangular frame that is 40 centimeters wide.
A
Source: Official Guide 2020
Solution:
Question Stem Analysis:
We need to determine the area of the mosaic, which is a hexagon comprised of 24 triangles of the same size and shape. Notice that if each triangle is an equilateral triangle and we are given a side of the triangle, then we can determine the area of one triangle and hence the areas of all 24 triangles, i.e., the area of the mosaic.
Statement One Alone:
Since we are given that each side of a triangular piece is 9 cm long, we know each triangle is an equilateral triangle. Therefore, we can determine the area of one triangle and hence the areas of all 24 triangles, i.e., the area of the mosaic. Statement one alone is sufficient.
Statement Two Alone:
Knowing the mosaic can be put inside a rectangular frame that is 40 centimeters wide is not sufficient to determine the area of the mosaic. The mosaic could be different sizes, as long it fits into the rectangular frame. However, since it can be different sizes, it can have different areas. Statement two alone is not sufficient.
Answer: A
