A board game uses a triangular piece measuring 3 inches on each side.

1 answer

It looks like you're referring to an equilateral triangle piece that measures 3 inches on each side. If you need information about its area, perimeter, or other properties, here’s a brief overview:

  1. Perimeter: The perimeter of an equilateral triangle can be calculated by multiplying the length of one side by 3. \[ \text{Perimeter} = 3 \times 3 \text{ inches} = 9 \text{ inches} \]

  2. Area: The area of an equilateral triangle can be calculated using the formula: \[ \text{Area} = \frac{\sqrt{3}}{4} s^2 \] where \(s\) is the length of a side. Plugging in the side length of 3 inches: \[ \text{Area} = \frac{\sqrt{3}}{4} \times (3)^2 = \frac{\sqrt{3}}{4} \times 9 = \frac{9\sqrt{3}}{4} \text{ square inches} \approx 3.897 \text{ square inches} \]

  3. Height: The height (or altitude) of an equilateral triangle can be calculated with the formula: \[ \text{Height} = \frac{\sqrt{3}}{2} s \] For a side length of 3 inches: \[ \text{Height} = \frac{\sqrt{3}}{2} \times 3 \approx 2.598 \text{ inches} \]

If you have a specific question or need more details about the triangular piece or the game itself, feel free to ask!