Final answer:
To calculate the area and perimeter of an equilateral triangle, we need to know the length of one side. In this case, the distance between the endpoints on the number line tells us that each side of the triangle measures 6 units. Using the formulas for area and perimeter, we can find that the area is 9√3 square units and the perimeter is 18 units.
Step-by-step explanation:
To calculate the area and perimeter of an equilateral triangle, we need to know the length of one side. Since the endpoints of the triangle are given as -2 and 4 on the number line, the distance between them is 4 - (-2) = 6 units. In an equilateral triangle, all sides are equal, so each side of this triangle measures 6 units.
To find the area of an equilateral triangle, we can use the formula: Area = (√3/4) * (side length)^2. Substituting the side length of 6 units into the formula, we get: Area = (√3/4) * 6^2 = (√3/4) * 36 = 9√3 square units.
To find the perimeter of an equilateral triangle, we can simply multiply the side length by 3. So the perimeter of this triangle is 6 * 3 = 18 units.