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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.
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Is this the simplest way to visually prove the "scalene trapezoid area formula"

Please refer to image. Is there a simpler way to visually prove the scalene trapezoid area formula?
Dave Kirkby
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Regarding Areas of volumes

I have a question: In general, area of square is Length times Length. If the length is less than $1$ then do we end up with less area? Like if we have a side whose length is $0.5\mathrm{m}$. Then the area is $0.25 \mathrm{m}^2$. That doesn't make…
MR. Raindrop
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Closed-form representation of area below a function

Let $f:[0,1]\rightarrow[0,1]$. $f$ is strictly increasing in $x$ if $x\in[0,x^*]$ and strictly decreases otherwise. Suppose that I'm interested in finding the area of the domain where $f(x)\leq t$. That is, if $$t=f(x)=f(x+y)$$ for some $t$,…
Greenteamaniac
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Area from Double Integral

I have solved this problem. I wish to find out if my solution is correct. Problem: Determine the area of the surface $A$ of the paraboloid: $$x^2+y^2-2z=0$$ where $x^2+y^2\le 8$, $y\ge x$ Solution: From the surface:…
Soso
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Surface Area of a Horn Torus

I have seen similar questions be asked but I'm uncertain if the same principles work for a horn torus. The question I have to ask has to do with Part (iii) of the following question. For Part (i) I stated that the expression is valid for $0 ≤ \theta…
Shomari Mills-Legerton
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area of a parallelogram spanned by (a,b) and (c,d) (positive oriented)

I know that the area of a parallelogram spanned by (a,b) and (c,d) is |ad-bc|. My teacher proved this formula in class and told us that it would be just ad-bc if (a,b) and (c,d) are positive oriented but he did not explain why. I tried to prove…
Anson Ng
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Area of a Surface of Revolution over Y-Axis

I need to set up an integral for the area of a surface rotated over both the x-axis and the y-axis. Given $y = e^{-x^2}$ over the interval $-1 \leq x \leq 1$. I'm having difficulty, however, finding this equation when rotating over the $y$-axis,…
user465188
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Surface area of irregualar shape

How to find the surface area of an irregular shape like this
AlgorithimicDUMB
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How to calculate the grey area of this irregular five-pointed star?

The corners of a five-pointed star lie on the sides of a square ABCD with the side length 1, that two corners of the star coincide with the corner points A and D. Further corner points of the star lie in each case in the interior of the edges AB,…
Liz Veras
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Find area of a quadrilateral inside a rectangle

I am asked to find the area of the shaded portion of the rectangle ABCD, whre $AD=5$, $AB=4$ and $E$ is the midpoint of $BC$. I know that if I subtract $\triangle ABC+\triangle AFD - \triangle AFG$ to the total area of the rectangle I get the answer…
Rafa U U
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From a square of unit length,pieces from the corners are removed to form a regular octagon.Then, the value of area removed is?

I'm having so much problem calculating the area, can anyone help?
Iti Shree
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Area betwen function and $x$-axis

If $f(x)=\min\left\{{\sqrt{1-x^2 /4},e^{-x}}\right\}$ where x belongs to [-2,2]. We have to find the area between the curve and $x$-axis . I found the area between $(-2,0)$ to $(0,0)$. But in the first quadrant I am unable to find their intersection…
user135482
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How do I calculate the length and width for a known area and ratio?

I have a rectangle with a known area and a known ratio of length/width. How do I calculate the length and width. Area: 1500 sq ft Ratio: 241 / 625 = .386 How do I calculate the length and width in feet.
D_Bester
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Find all possible integer dimension equiareas inside a fixed rectangle

The problem in the general case with arbitrary values is likely pretty difficult, so I limit the scope of this question to this specific problem: Consider a rectangle with width 30 and height 16. Divide it into 12 pieces with equal area, and…
Mateen Ulhaq
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