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

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Area of all triangles involved in a big triangle.

I have a big triangle made up of several small triangle as depicted in picture given below. Suppose, there is one generic triangle of this shape which is formed by joining points arranged in n rows....
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Sum of Area of Circles. [duplicate]

A circle of radius x cm is inscribed in an equilateral triangle and is tangent at three points. Three smaller circles are inscribed so that they are each tangent to two sides of the triangle and to ...
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In the figure below,three congurent semicircles with centres P,RQ,R are drawn on each side of three equilateral triangle.Find shaded part's area?

In the figure below,three congurent semicircles with centres P,RQ,R are drawn on each side of three equilateral triangle.Find shaded part's area?
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Find equal side lengths for isosceles triangle from middle angle and area?

I know that this is a really easy question, but I am looking for the answer to this question: The area of this isosceles triangle is 5cm squared. The angle ABC is 22 degrees. Work out ...
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Point A is picked randomly in a circle with a radius of 1, and center O. What is the variance of length OA?

Point A is picked randomly in a circle with a radius of 1, and center O. What is the variance of length OA? I believe the CDF has to found first, then we need differentiate it, find the expected ...
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27 views

$N$-dimensional volume (of revolution)

Consider the system of coordinates $\{x_{1},x_{2},...,x_{n}\}$ and an n-dimensional shape such that, in $\{x_{1},x_{n}\}$ (and $x_{2}=x_{3}=...=x_{n-1}=0$) it is inside the lines $x_{n}=ax_{1}+b$ and $...
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49 views

How can integrals be developed? [closed]

I wonder if it would be possible to develop integrals without any use of simple functions and "area approaches". Thank you.
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33 views

Find radius of circle (or sphere) given segment area (or cap volume) and chord length

The goal is to design a container (partial sphere) of given volume which attached to a plane via a port of a given radius. I believe this can be done as follows but the calculation is causing me ...
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33 views

Calculate Section (area) of N-Dimensional Tube

I have the following n-dimensional shape $1=\sum_{i=1}^{n}a_{i}x_{i}^{2}$ where $a_{i}>0$ and I'd like to calculate the cross-section area inside. Any suggestion? Note: I call it an $n$-...
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10 views

Find the average of points/areas in a chart

I've calculate areas at certain points along X. The X axis is along a beam and these areas are the required area of steel at ...
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2answers
36 views

Find the area of $S=\{(x,y)|\rm{\exists ~}\theta,\beta,x=\sin^2{\theta}+\sin{\beta},y=\cos^2{\theta}+\cos{\beta}\}$

Let $S$ be the domain defined by $$S=\{(x,y)|\rm{\exists ~}\theta,\beta,x=\sin^2{\theta}+\sin{\beta},y=\cos^2{\theta}+\cos{\beta}\}$$ find the area of $S$ This is middle school problem,so I think it ...
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1answer
20 views

Spaces relations

I have a physics question for which I need to determine the radius of a circle. Given are two Ellipse shapes with the same center (0,0 in a Cartesian space). the Height and Width of the smaller is 1[...
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1answer
31 views

Calculate the area of a sphere drilled by two cylinders.

Let $S$ be the sphere given by the equation $x^2+y^2 +z^2 =4$ cut with $z \geq 0$. Now, we drill the semisphere that is left with two vertical cylinders of radius $1$, whose axes are respectively ...
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42 views

Surface area of a bottle with integration

Would it be possible to model a bottle using a function, then revolving it to determine the surface area and the volume while customizing the curvature and the dimensions of particular sections of the ...
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1answer
93 views

Find Minimum area of given hexagon. Geometry Question.

It has been a year Since I am searching for an answer to this question. This question was probably asked in International Mathematics Olympiad but I am not a 100% sure. Q : ABCDEF Is a concave ...
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1answer
20 views

The Area of Card Required to Make a Cone

The solution of the question I'm trying to understand is this: The part of the solution I don't understand is "the area of card needed for each hat (cone) is $\frac{1}{2}r^2$", because I would ...
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2answers
73 views

Compute the area of a oval based 2d geometry

I know that the area of a shape generated as below $R=r_0+a_1\cos(\theta)+a_2\cos(2\theta)+a_3\cos(3\theta)+...$ Where you can plot it and see the area value in matlab by: ...
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1answer
51 views

Area bounded by the x-axis and the curve..

Find the area bounded by the $x$ axis and the curve $$y = \frac{(x^2−x−2)}{(x^3+8)}$$ between its points of intersection with the $x$ axis. So point of intersection are $(-1,2)$ since $$f(y)=0$$ when ...
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1answer
26 views

Riemann sum problem

I'm confused on how $2[4+0+0.4+1.6+3.6]$ is arrived at instead of $2[1+1.4+2.6+4.6]$
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1answer
55 views

Using small spherical balls to fill a cube and also find volume of the cube

Is it possible to calculate volume of a cube (with volume $L^3$) by filling it with small balls each with a radius $r_N$ and the balls are disjoint. Let the number of balls be $N$ $$\lim\limits_{N\...
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28 views

Surface of 4D implicit function

I have a 4D implicit function in form $$f(x,y,z) = w $$ which can be rewritten to $$ g(x,y,z, f(x,y,z)) = 0 $$ So it is not "full 4D", but rahre a 3.5D space. How can I compute area of $g$ within ...
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122 views

What is the area very deep meaning?

For example, Why we say : If one side of the square is $a$ then $a^2$ is the area of the square. What is the meaning of area in complex space? Can you explain academically, this meaning?
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83 views

Dodecagon Area Question

The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon. Is there any way to do this without trigonometry? And could you include a proof also? :O
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24 views

why is area of a canvas being devided ?

Hey guy i am not so great at math and basically i have the following calculation that i need to figure out the entire formula ,looks like below: ...
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3answers
60 views

Integrate $\int^a_0x^3 - x \mathop{\mathrm{d}x}$ to find the area

(a) Solve the equation: $$\int^a_0x^3 - x \mathop{\mathrm{d}x} = 0, a > 0$$ (b) For this value of $a$, find the total area enclosed between the $x$-axis and the curve $y=x^3 - x$ for $0 \leq ...
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Area of a triangle whose vertices lie on a parallelogram

In the parallelogram $ABCD$, $X$ and $Y$ are the midpoints of $BC$ and $CD$. Then prove that $$Ar(\triangle AXY) = \frac {3}{8} Ar(ABCD)$$ My Attempt : Construction; Joining $BY$ and $AC$, I got ...
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1answer
34 views

Proving area equal to zero of a continuos function.

I'm kinda stuck with this exercise: Prove that the graph of a (uniformly) continuous function $f\:[a,b] \to \mathbb{R}$ has area zero. I was thinking that maybe I should use uniform continuity ...
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1answer
16 views

Derive the length of the longest line segment that can be enclosed inside the region A.

Q. Let A be the region in the xy-plane given by A={(x,y): x=u+v, y=v, u^2+v^2≤1}. Derive the length of the longest line segment that can be enclosed inside region A. My attempt: I found the equation ...
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1answer
25 views

Complex Solids of Revolution

I know that to compute a solid of revolution of a function $f(x)$ rotated around the $y$-axis, one method we can use is the "shell" method. For example, $f(x)=1/4x^2\in [2,4]$, rotated around the $y$-...
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1answer
24 views

Proof - Percentage change in area if side of a two dimensional figure is increased by $x\%$

If each of side of a rectangle or any two dimensional shape is increased by $x\%$, its area is increased by $\left(\dfrac{x^2}{100}+2x\right)\%$ Source: careerbless.com I am trying to ...
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Computing the area of the surface between two polylines

Consider two 3D polylines, A and B. I am interested in computing a distance/similarity between them (from their current positions, no need to find the "best overlap" first). I have come up with some ...
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38 views

How to find area of isosceles triangle when given two heights? [closed]

So I know the sine and cosine theorem and I tried using them but I got nowhere. (I got to an equation which I can't solve and I know there must be an easier method since we have not studied how to ...
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2answers
60 views

Determine the value of c that makes the blue area above y = c equal to the blue area below y = c.

Determine the value of c that makes the blue area above y = c equal to the blue area below y = c. edit: I'm kind of stuck on this problem, not sure what steps to do so that I can find the equal areas....
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Calculate the percentage of a triangle inside a cuboid?

I have a large (order 10^7) collection of triangles in 3D space. I also have a cuboidal mesh also of order 10^7. For each triangle I need to calculate the area of that triangle which is inside any of ...
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A criterion for area preserving dynamical system

In my investigation of dynamical systems I was met with this seemingly easy question I could not find an answer to: If we have a two dimensional system of autonomous ODEs viewed as a 2D dynamical ...
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1answer
26 views

Maximum area of a triangle when perimeter is fixed.

I can't solve the following problem: Show that amongst all triangles with perimeter $3p,$ the equilateral triangle with side $p$ has the largest area. Further show that $9p^2\ge 12\sqrt{3}\Delta.$ ...
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1answer
23 views

Area of a surface - surface integral

I am trying to find the area of a surface, but I can't describe the domain of integration correctly. The surface is part of the cylinder $x^2+z^2=a^2$ inside $x^2+y^2=a^2$. Here is what I have done so ...
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2answers
108 views

Minimum Area of An Ellipse Surrounding Four Circles

The circles are all four combinations of $(x\pm60)^2+(y\pm25)^2=5^2$ (see pic at end). The ellipse I've got is one I found via trial and error but there must be an analytical way to solve this, right?...
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1answer
18 views

Find range of values for a square's area.

This is question is from my practice final exam. The perimeter of a square is to be between 20 meters and 60 meters. What is the range of values for its area?
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22 views

Quadratic polynomials in variables x,yx,y

I have two equations which define 2-order areas I have to determine matrix, eigenvalues, definiteness and area. I determine first three things, but how can I find out which area is it? Example 1. $...
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1answer
27 views

How big do squares need to be to fit a box, tesselating, with minimal remainder?

A geometry question that I feel utterly defeated by. I'm trying to design a responsive user interface that efficiently fits a variable number of square elements on a screen, by adjusting the size of ...
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53 views

Why is the area of a rectangle given as $l\times h$? [duplicate]

While this may seem like a simple question, I have found it very difficult to answer. My question is "Why is the area of a rectangle given as $l\times h$?" We define area as the "size of a two ...
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Number of rectangles to cover a circle

After searching around I found this is similiar to the Gauss Circle but different enough (for me anyway) that it doesn't translate well. I have a circle, radius of 9 that I need to completely cover ...
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1answer
41 views

How do i calculate the area of shaded region?

I wouldn like to find the area of shaded region which it's circulated by a triangle as show in the below picture ? Note: I tried to draw other circle arround triangle ,but it's seems hard to me to ...
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3answers
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Same perimeter and area for a circle and an ellipse

For a given circle, is there exist an ellipse with same perimeter and area as to that circle? If not, that is my suspicion, is in three-dimension parallel question: For a given sphere, is there ...
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1answer
44 views

Formula for area of triangle in complex plane [closed]

If $A(z_1)$, $B(z_2)$, $C(z_3)$ are vertices of a triangle $ABC$ in Argand plane, what is the area of the triangle?
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39 views

Calculate area of a figure on the picture

What kind of figure is it? (the filled one). How can I calculate it's area? Known: radius of each circle and coordinates of their centers. Picture of this figure
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21 views

How to find the limits of integration for parametric

In this question: Find the area bounded by: $x=\ln(t)$, $y=\frac{t-3}{t-1}$, $3\leq x \leq 5$, and by the $x$-axis (it is above the $x$ axis). I solved the integration parametric curve, $3\ln(t) -...
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1answer
21 views

Problem with applying differentiation

I am working on the solution of the following problem. A cylinder has a flat base on one end, and a hemispherical top on the other. The material used for the hemisphere is twice the cost of the ...
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50 views

Question about area and triangle

Problem: Consider the following diagram. in $\triangle$ABC: Areas: $\triangle$AOM = a $\triangle$POC = b $\triangle$NOC = c $\triangle$BON = d. Find the area of $\triangle$MOB and $\...