# 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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### Determine the area bounded by the curves $y=2x$ and $y=x^2$ and the parabaloid $z=x^2+y^2$

Determine the area bounded by the curves $y=2x$ and $y=x^2$ and the parabaloid $z=x^2+y^2$ I'm not really sure what my function that I'm integrating is supposed to be I believe I want to integrate on ...
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### How can I determine the area of the region bounded by the curve $x^2=y^4(1-y^3)$ [closed]

$x^2=y^4(1-y^3)$ On a graph it looks like a diamond. This is for my integral calculus class.
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### Bounded Area between $y=x^2$, and $y=9$, and $y=k$

I have been given a function to find the horizontal line $y=k$ which would splice the area bounded between $y=x^2$, and $y=9$, into two equal parts. I approached the function using symmetry to find ...
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### How to tell the run of a line segment where the area underneath it, starting point, and slope are known.

I have a program where I am currently solving for the difference of X₁ and X₂ of a line-segment where the area under the line-segment (A), the slope (s), and the starting point (X₁,Y₁) are known. ...
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### Surface area of ellipsoid created by rotation of parametric curve

I have a parametric curve (elipse) defined as follows \begin{aligned} x(t) &= \cos(t)\\ y(t) &= 2 \sin(t)\end{aligned} and need to calculate the surface area of the ellipsoid produced by ...
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### Solid of revolution using washer method(Gives negative answer)

My teacher even knew that the answer should not be negative but it turned out to be negative. The given was y=x^2, y=4x-x^2, revolving about the y-axis. Here are some of the solution presented, I hope ...
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### Generalizing computation of number of pixels in inscribed circle to axis-aligned ellipses at arbitrary points

This answer really nicely sums up the question of how to compute the number of pixels inside an inscribed circle. However, I am looking for a more generalized version of this in two ways. 1) I would ...
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### Proof for area of an equilateral triangle with respect to one side?

I'm trying to find out the area of an equilateral triangle with respect to one side. Anything wrong with my proof? An equilateral triangle with sides of length $a$ can be divided in half along the ...
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### Inequalities about area and perimeter

"A gardener is laying out a rectangular lawn. His specifications are that the area $(A)$ must be greater than $40$cm but the perimeter $(P)$ must be less than $40$cm. if the width of the lawn $(w)$ ...
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### Help indentifying unknown method of computing area by rolling a ball about the perimeter

Some time ago I saw a brief presentation about a newly discovered method used to compute the area of certain two-dimensional shapes by rolling a circle (of varying radius) about the perimeter; the ...
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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?
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### Find area of the fourth triangle given the area of three triangles.

This is the question that I got in TCS Ninja under the Quantitative section. How shall I do this? Help !!
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### What is the area of this figure?

I want to know how to find the area of this shape: Yellow, white and blue shapes are ellipses. Red is a square. The blue ellipse is not cut in half by the square. I know that I have to add up all ...
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### Area of a circle segment on sphere, given radius (meters) and central angle (degrees)

Situation I have a circle segment and some information about the circle it belongs to. Given Information: radius of the circle in meters central angle in degrees lat/long of all three points on the ...
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### How to double the circle?

I'm looking for a compass-and-straightedge method to construct a circle that has area twice of the area of another circle, with no prior knowledge of π, without knowledge of the formula for the area ...
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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 ...
In $ABCD$ tetragon $E$ and $F$ are mid points of $AB$ and $AD$ respectively. $CF$ intersects $BD$ at point $G$. If $\angle FGD = \angle AEF$ and the area of $ABCD$ is $24$ , what is the area of $... 1answer 84 views ### 1000cm^3 of metal is to be cast as a rectangular block with square ends (Calculus Optimization question) 1000cm^3 of metal is to be cast as a rectangular block with square ends. Use calculus to show that for the least surface area a rectangular the rectangular block needs to be a cube. Having some ... 1answer 43 views ### Area of a triangle in space using determinants from 3 points I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look? Thanks 1answer 156 views ### Calculate surface normal and area for a non-planar quadrilateral Given the four coordinates of the vertices, what is the best possible approximation to calculate surface area and outward normal for a quad? I currently join the midpoints of the sides, thus ... 1answer 49 views ### Calculating integral over unit ball using co area formula Calculate$\int_V\frac{1}{2+(x^2+y^2+z^2)^{\frac{3}{2}}}dxdydz$, where$V=\{(x,y,z)|x^2+y^2+z^2\lt 1\}$using the co area formula. So I know that the formula is:$\int_V f dx$=$\int_a^b\int_{M_c}\...
Find the area of the colored octagon (tell the ratio between square $ABCD$ and the colored polygon). Square $ABCD$ is a perfect square, and $E,F,G,H$ are the midpoints of the line they are ...