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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what is the proper way of writing 1 square millimeter?

(.001m)^2 or (.001m^2) I think it is the first one but Im not sure. Please look over these equations for me so I can have a sufficiently long question to submit.
User3910
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Area bounded by line and curve

Find the total area of the finite domains bounded between the curve $y=x^3−4x$ and the line $x+2y=2$. I have sketched a graph of the curve and the line and found the points they intersect they $x$-axis and $y$-axis by equating them to 0. Afterwards,…
Thomas King
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How to calculate the distance inside this 45deg rectangle

What is the easiest arithmetic to get the 168px distance marked in red in the rectangle based on a square which is 340px width x 577px height and rotated 45 deg ? I came to the solution: 168px doing the following calculation: (577px / square root of…
Martin
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Area of the figure formed- the edges being chipped off forever

Consider a random figure. Let's say a regular hexagon ($6$- sided polygon) of area $6$. Chip off the $6$ corners to get a dodecagon ($12$ sided polygon). And repreat this chipping process forever. Basically the number of sides will get twice the…
Mathejunior
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Exact surface area by rotating about the x-axis

I'm trying to find the surface area by revolving this equation around the x-axis from 0 to 3. $$y^2=x+1$$ I get the answer $$\frac \pi 6 (17\sqrt{17}-5\sqrt5)$$ The answer is correct according to Wolframalpha but my book says the answer is $$\frac…
Brady Dean
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Split circle in pairs parts of equal area

Birthday cake: Two fiends A, B are going to share a circular cake, as follows: They alternate turns doing a straight cut each, starting by A and doing 4 cuts in total. Then they take turns picking one piece at a time, again starting from A. Can you…
Alex.vollenga
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How to calculate area of a plot of land from a photo (with acceptable error rate)?

I want to calculate the area enclosed by the yellow lines. It also needs to account for the missing piece of land out of the picture by extending the yellow lines. Since no scale is given, I guess we have to assume some scale (error rate up to few…
Aye_Caramba
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area between two curves . not able to plot the curves

I have to find the area between the curves $x^2=y^3$ and $x=y$. How do I plot the curve $x^2=y^3$?. I have no experience if working with such curves. The only thing i have been able to do till now is find the intersection points $(0,0)$ and…
joey lang
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Is there a formula to find out the perimeter of an irregular shape on lattice points when you already know the area?

Is there a formula to find out the perimeter of an irregular shape on lattice points when you already know the area? I am asking this as I have a test tomorrow, and one of the questions that could come up is the area/perimeter of an irregular…
bio
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Finding the Area of an Ellipse using the Formula

I'm preparing for the ACTM Sate contest, and I stumbled across this problem. I've never learned how to decipher equations like this, so could someone explain what these equations mean and how to solve this problem? The area of an ellipse is…
Alice Cai
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Scaling a kite, effect on area

What happens to the area of a kite if you double the length of ONE of the diagonals? What happens to the area of a kite if you double the length of BOTH diagonals?
Danneh Corn
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Find area enclosed?

Surface $S_1$ is formed by $|x-1|≤ 1$ and $|y-2|≤ 3$. Surface $S_2$ is formed by $x ≥3$, $y ≤1$ and $x+2y ≤3$. S is union of $S_1$ and $ S_2$. Find the area of surface $S_1$, $S_2$ and $S$ ?
Taylor
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The difference of the diameter and circumference

The difference of the diameter and circumference of base of a cone is $30$ cm. If the slant height of the cone is $25$cm, find the total surface area of the cone. My attempt, If $r$ is the radius, $$\frac {r}{2} - 2\pi r=30$$ $$r=\frac…
pi-π
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Area (or volume) of polygon inscribing a distribution of points/Finding vertices of distribution

I am trying to compute the (maximum) area/volume of a 2D/3D distribution of points. However, I'm struggling to define the outliar points in such distributions without resorting to very bad spaghetti code that will be very inefficient. So given a 2D…
catubc
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Fill up a surface with rectangles

First of all, sorry if this is a simple question. I am programmer and facing a problem about calculation. I have rectangle surface ($x_{s}$) with height $h_{s}$ and width $w_{s}$ and I want to put $n$ rectangles ($x_{n}$) with same height $h_{n}$…
Joshua
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