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What is the opposite of sparsely?
Sparsely usually means appearing only occasionally, for example a sparsely populated area has only a few people living there. The opposite would be things compacted into a small area, so the opposite of sparsely would be 'densely'
In math what is the definition of fixed area?
I think a fixed area is a preset area kinda. Like that's the only bit of info you have, so you can make a whole bunch of rectangles. At least, I think.
Is it possible to make a shape out of the area of 16 and a perimeter of 15?
Yes but not a square (or rectangle). A quadrilateral with an area of 16 sq units must have sides of at least 4 units and so a perimeter of at least 16 units. However, a circle of perimeter 15 units will enclose an area of 17.905 sq units (to 3 dp) so an ellipse of 15 units' perimeter will meet the requirements.
Why can't a polygon have only 2 vertices?
A polygon is a plane shape in which an area is enclosed by straight lines that meet pairwise. Two lines cannot enclose an area. Either they are parallel and there are two gaps to the area between them or they meet at an angle and there is a gap in the enclosure opposite the angle. So there must be at least three sides. Now three lines, taken two at a time create three distinct vertices (a triangle). So the least number of vertices is 3.
What is the least perimeter of a rectangle with an area of 32 square ft?
The least perimeter is attained when the rectangle is, in fact a square. A square with an area of 32 square feet will have sides of sqrt(32) = 4*sqrt(2) ft. So the perimeter of the square will by 4*4*sqrt(2) = 16*sqrt(2) = 22.63 feet, approx.
