# Questions tagged [area]

Area is a quantity that expresses the extent of a two-dimensional or three-dimensional surface or shape.

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### If $\text{Area} (A) = \text{Area} (B)$ and $\text{Perimeter}(A) = \text{Perimeter}(B) \implies A \cong B$?

If I have an $n$-gon $A$ and a convex $n$-gon $B$ with the same perimeter and the same area, does $A\cong B$? Edit : What becomes the answer if I replace convex by regular?
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### Related Rates Ladder Question

A ladder 25 feet in length creates a right triangle with the wall it's leaning against. If the base of the ladder is being pulled horizontally away from the wall at a rate of 2ft/s, what is the rate ...
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### Spherical Triangle

I know that the area for a spherical triangle is calculated as Area $= r^2(a+b+c-\pi)=r^2E$ where $E= (a+b+c-\pi)$ is the spherical excess I was wondering why do you have to multiply by $r^2$ (the ...
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### Measure of a set $A=\bigcup_{z_x,z_y} \{ (x,y) \in [0,1]^2 : |axz_x-byz_y| \le c \}$

What is the measure of the set $$A=\bigcup_{\substack{1 \le z_x \le N_x \\ 1 \le z_y \le N_y}} A(z_x,z_y)$$ where $A(z_x,z_y)=\{ (x,y) \in [0,1]^2 : \lvert axz_x-byz_y \rvert \le c \}$ for ...
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### Expressing the area as a function :)

Express the area A of an equilateral triangle as a function of the height of the triangle. Thanks :) I am not sure where to even start on how to answer this problem.
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### 2 calculus questions with integration - check me

I have 2 questions I would like assistance with. 1) Find the area of the region bounded by the graphs $y=5x, y=15x, y=\frac{4}{x}, y=\frac{8}{x}$ This was very difficult and tedious. I had trouble ...
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### $ABCD$ is a quadrilateral and $P,Q$ are midpoints of $CD, AB.$…

$ABCD$ is a quadrilateral and $P,Q$ are midpoints of $CD, AB.$ $AP$ and $DQ$ meet at $X, BP$ and $CQ$ meet at $Y.$ Prove that $$|ADX|+|BCY|=|PXQY|$$ (here $|N|$ means area of the shape $N$) I have ...
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### Looking for some intuition behind why the area enclosed by a simple closed curve $C$ can be obtained by computing $\frac{1}{2i}\int_C {\bar{z}} \ dz$.

By some manipulation and an application of Green's Theorem, I am able to show that $$Area = \frac{1}{2i}\int_C {\bar{z}} \ dz$$ To me, this seems to be an unexpected result. Is there some intuition ...
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### 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 ...
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### Area of convex hull of 6 points greater than twice the sum of the areas of 2 triangles formed by the 6 points

I noticed something interesting but I couldn't prove it to the end. I want to prove that if I have $6$ coplanar points and the area of convex hull of these points is equal to $P$, then I can mark the ...
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### Area of triangle given 3 equations of sides, without finding points of intersection [duplicate]

Can anyone tell me a way to calculate area of a triangle given the equations of its 3 sides without sketching or finding the points of intersection?
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### Area of a square inscribed in a circle

ABCD is a square inscribed in a circle whose diameter is L cm. If P and Q are mid points of BC and CD, respectively, find the shaded area MDCNT Thanks I tried this If I knew the M value I could ...
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### Equiareal Voronoi tessellation

I'm interested in even (or "proportional") disrtributions of points on 2D areas. Here is the initial question, but many others ideas appeared later. Centroidal Voronoi tessellation is well known ...
If the lines intersect the vertices of the square. The area of the square is $1$ and the lines also intersect the midpoints of the square lines. How to find the area of shaded region?