When an equilateral triangle is rotated about a line that runs parallel to one of its sides, the resulting shape is a triangular prism. In this case, if we consider a triangle where its base lies along the line of rotation and the triangle revolves around this line, it creates a solid 3D object that has two triangular faces and three rectangular lateral faces.
Now, to find the approximate circumference of the base of this shape, we first need to establish the relationship between the dimensions of the triangle and the distance of rotation. Let’s break it down:
- The circumradius (R) of the equilateral triangle can be calculated using the formula: R = a / (sqrt(3)), where ‘a’ is the side length. In this case, ‘a’ is 20 mm.
- Thus, R = 20 mm / (sqrt(3)) ≈ 11.55 mm.
- The circumference (C) of the circle at the base, which is formed by the rotation of the triangle, can be calculated using the formula for the circumference of a circle: C = 2 * π * R.
- Substituting the value of R, we get C ≈ 2 * π * 11.55 mm ≈ 72.54 mm.
Therefore, when rotating the equilateral triangle, the shape created is a triangular prism, and the approximate circumference of the base, formed by its rotation, is about 72.54 mm.