Video narration
How do you find the area of a circle when an equilateral triangle with side six sits inside it? Picture a round plate, with the triangle's three corners touching its rim. The side tells you the circle's radius, but not directly: for an equilateral triangle, the radius is the side divided by square root of three. Here, that means six divided by square root of three, which simplifies to two square root of three units. That's the distance from the plate's center to its edge-not six, so keep that radius for the next step. Circle area is pi times the radius squared. Substitute two square root of three: pi times (two square root of three) squared. Squaring gives four times three, so the radius squared is twelve. Multiply twelve by pi. The round plate's area is 12π square units-about 37.7 square units.