Why is the area of a circle measured in ''square units'' when a circle isn't square?

Answer 1

haha this is kinda of funny but lets see if i can explain...

the area means the amount of space inside an object. a circle is alot different from other objects since it has no edges like a square or rectangular shaped object. a circle is measure in degrees... 360 degrees for a whole circle. the greek letter pi was formulated to help out with the understanding of a circle. pi is a number that goes on infinitely with no repeats in its decimal.

I don't know what your math background is but in Calculus II in college we heavily learned about integrals. an integral is the amount of space under a line or in our case a curve. the circle is actually an infinite curve. if you take the integral it is never completely accurate. there is always some margin of error when you take the decimal places out very far. but this is still used because the error will be so small it is negligible. just like if you take pi out to a trillion places, this would be negligible because it is not going to affect anything at this small of scale

now imagine taking the integral of a whole circle. taking the integral means you use small rectangles and line them up straightly inside the circle. you need to use very small rectangles to get an accurate reading of the area of a circle. when you put smaller and more rectangles in the circle you minimize the amount of free space left over near the edges of the circle. lets say you put one trillion rectangles side by side in the circle. then you took a magnifying glass and looked at the edge of the circles. you would see small rectangle edges up against the circle edge. (it is so much easier explaining integrals in person lol)

Since you are taking the integral you are actually taking the area of small rectangles and rectangles do have square units and is a quadrilateral like a square which also has square units.