Articles of area

Minimum area of Inscribed Square

GRE study guide asks The perimeter of square S is 40. Square T is inscribed in square S. What is the least possible area of square T? Choices are 45 48 49 50 52 They say answer is 50. How do they even get this? T has lengths less than 10, so it can be […]

Proof that for any n-sided polygon P, and any integer m greater than n, there is an m-sided polygon with the same area and perimeter as P?

The answers to a recent question established that it is possible to construct families of polygons all with the same area and perimeter. Some comments on some of the answers inspired this very specific question: Prove that for any n-sided polygon P, and any integer m greater than n, there is an m-sided polygon with […]

How to find area of remaining square with shapes inside

Pretty much there is a square with a height and width of $2$”, inside there is a perfect circle with radius $1$”. Also overlapping the circle and square is a isosceles triangle also with height $2$” and width of the bottom to be $2$”. (Truly to see what I’m talking about, you have to click […]

How to draw diagram for line and parabola.

I am finding the area bounded by parabola and line using definite integral. When its about line y = x and parabola $y^2 = x$. I know the line passes through origin. But when we have given equation of line like x = 4y – 2 and parabola $x^2 = 4y$ I got confused how […]

Triangle Quadrilateral and pentagon whose areas form a set of consecutive positive integers.

Find a triangle, quadrilateral and pentagon with integer side lengths whose areas form a set of three consecutive positive integers. Make the areas as small as possible subject to these constraints. Report you answer by giving the areas of each figure with the side lengths of those figure? We use a rectangle for our quadrilateral […]

Maximum area enclosure given side lengths

A peer of mine gave me the following problem : Given a sequence of $n$ lengths (i.e.,$L_1, L_2, .., L_n$ ) where each is the length of the side, find a sequence of $n$ points (where $p_k = (x_k, y_k)$) such that $dist(p_k, p_{k+1}) = L_k$ and $dist(p_1, p_n) = L_n$ where $dist(a, b)$ is […]

Area covered by Moving Circle?

Consider a situation where we have a point (x,y) moving on a 2-D plane. In fact, the point is function of time x=f(t),y=g(t). Centered around (x,y) is a circle of radius r? Obviously, we can visualize a circle moving in the 2-D plane. Compute the area covered by the circle from the the start of […]

Calculate the viewing-angle on a square (3d-calc)

I’m in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 coordinates of the shape, and I already had an idea: You could have a look on the […]

Area under parabola using geometry

We have to find the area of the pink region. As we all know this can be evaluated using limiting its Riemann sum, of which its a standard example. However I want to know if this can be done without using calculus, with directly using geometry. I think it would be very interesting challenge, but […]

What is the least number of (fixed) parameters I can ask for, when calculating area of a triangle of unknown type?

I need to calculate the area of a triangle, but I don’t know, whether it is right angled, isoscele or equilateral. What parameters do I need to calculate the area of a triangle of unknown type?