Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [area]

Area is a quantity that expresses the measurement of the extent of a two-dimensional shape.

Frequent problems related to area include

  • Computing area of planar figures like triangles, circles, quadrilaterals, etc.
  • Computing the surface area of a figure in three dimensional space like a sphere or a cube.
  • Applying techniques of integral calculus to calculate the area bounded underneath the graph of a function, or the area bounded between the graphs of two functions.
  • Broadly discussing alternative definitions and notions of area.
3695 questions
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Why square units?

I was recently asked "Why is the area of a circle irrational?", to which I replied that it was not necessarily irrational—there are of course certain values for $r$ that would make $\pi r^2$ rational. She proceeded to clarify, "But the area of a…
Fengyang Wang
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How to find the area of any irregular shape?

how to find the area of any irregular shapes without dividing it into smaller regular shapes ? Example Image:
Premnath D
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fish tank problem

A rectangular swimming pool with dimensions of 11m and 8m is built in a rectangular backyard. The area of the backyard is 1120m^2. If the strip of yard surrounding the pool is of uniform width, how wide is the strip? So I tried to find a diagram but…
joko34
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Area of a five pointed star

A 5 pointed star is inscribed in a circle of radius $r$. Prove that the area of the star is $$ \frac{10 \tan\left(\tfrac{\pi}{10}\right)}{3-\tan^2\left(\tfrac{\pi}{10}\right)} r^2 $$
Rudstar
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Area enclosed by $\sin^2(\pi x)+\sin^2(\pi y)>1$ and $x,y\in[-1,1]$

The area of regin traced by the point in the cartesian plane which satisfy the equation $\sin^2(\pi x)+\sin^2(\pi y)>1$ , where $x,y\in[-1,1]$ My Try: We can write $\sin^2(\pi x)+\sin^2(\pi y)>1\Longrightarrow 2\sin^2(\pi x)+2\sin^2(\pi…
jacky
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How did Archimedes figure out that the area of ball is the same with the area of cylinder surrounding it?

https://www.varsitytutors.com/hotmath/hotmath_help/topics/surface-area-of-a-sphere This one says the area of a ball is the same with the are of cylinder surrounding it. Why?
user4951
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Area below the curve $y=\left[\sqrt{2+2\cos2x}\right]$

Find the area below the curve $y=[\sqrt{2+2\cos2x}]$ and above the $x$-axis , $x\in [-3\pi,6\pi]$, (where $[.]$ denotes the greatest integer function) . My…
Abhishek Kumar
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Finding the area enclosed by curve defined by $\arcsin x+\arcsin y=\arcsin(x\sqrt{1-y^2}+y\sqrt{1-x^2})$

If $\arcsin x+\arcsin y=\arcsin(x\sqrt{1-y^2}+y\sqrt{1-x^2})$ Then the area represented by the locus of point $(x,y)$ if it is given that $|x|,|y|\leq 1$ My Try: Put $x=\sin \alpha$ and $y=\sin \beta $ and $\alpha,\beta \in [-90^\circ,90^\circ]$…
DXT
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Polygon area method

I saw this problem in a puzzle book. Just wondering if anyone can explain the principle behind this method. A rectilinear figure of any number of sides can be reduced to a triangle of equal area, and as $\angle AGF$ happens to be a right-angle the…
Peter
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Finding the area inside the plot $x^4+y^4=x^2+y^2$

Find the area inside the plot $x^4+y^4=x^2+y^2$.
dienhosp3
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Area of ellipse which is not in standard form

By graphing device i understand that $x^2+xy+y^2=1$ is ellipse. By some geometry i find area of above ellipse which comes out $\pi$ (is it right?), but it was easy case. Is there any quick method or standard formula to calculate it or we have to…
ogirkar
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How to calculate an area under $y=x^{-2}$ without integral

I need to get a formula for area under $y=x^{-2}$ for $x \in (1,a)$, where $a \in (1, +\infty)$, WITHOUT using integrals. I tried following: Let $h=\frac{a}{n}$, where $n$ is natural number of sections you got by dividing abscissa from $1$ to $a$…
Levon Minasian
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Area of eye-shaped curve $\sin^4(x) + (\cos(y) - 3)^2 - 16 = 0$

I would like to calculate the area of the eye-shaped curve created by the following equation: $$ \sin^4(x) + (\cos(y) - 3)^2 - 16 = 0 $$ If we plot this equation we get: So the idea is to calculate the area of one of those "eyes" in the image. The…
HugoTeixeira
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Area of the shaded part.

My Attempt, Area of square $=10^2=100 cm^2$. Area of circle $=\pi r^2=25\pi cm^2$. What should I do further?
pi-π
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Surface area of house

This is the image: So the question is: (a) Ralph is painting the barn, including the sides and roof. He wants to know how much paint to purchase. What is the total surface area that he is going to be painting? Round to the nearest hundredth. (b) If…
John Doe
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