How do you find the area of an equilateral triangle with a 6-inch radius?
1 Answer
Based on this image...
Explanation:
...we can call segment "a" the radius, and if we do that, we calculate the area of the triangle as follows:
Look at the vertical line bisecting the triangle, made up of segments of length "a" and "h"
Now look at the smaller, right triangle towards the bottom left of the equilateral triangle, with sides "a", "h", and "S/2".
If we're taking "a" to be the radius (in our case 6 inches), then
The original equilateral triangle in the figure is bisected by the vertical line, making 2 right triangles of height 9 inches and a base of length S/2.
So, the original equilateral triangle in the figure is twice the area of this larger right triangle. A right triangle's area is
...which works out to:
46.77 square inches (rounding)
GOOD LUCK