Questions tagged [area]
Area is a quantity that expresses the extent of a two-dimensional or three-dimensional surface or shape.
2,345
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How to find which area is bounded by those two graphs
Namely we have given two graphs: $y=\sqrt{2 - x^2} \text {and } x + (\sqrt{2}-1)y = \sqrt{2}$
The question asks us to find the area bounded by those two graphs. I tried sketching those two graphs in ...
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1answer
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area of a helix [on hold]
is anyone knows how to calculate the area of a ring that is twisted, for example an edge of a tooth of a thread coil, please see a picture (area between A and B points)
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how to convert Square meter to Meter? [on hold]
i know Square Meter is are but i want to know how to calculate Square meter to Meter
for eg: i have 84 Square meter area then i want to know how many meter will ...
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1answer
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+300
What is the expected number of random small circles it takes to cover a large circle?
I have a large circle of radius $B$. I choose a random point inside the large circle, and draw a small circle of radius $A$ around it ($A<B$). What are the chances that, after drawing $n$ such ...
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1answer
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Show that the Area of a Triangle is Less than the Sector it is Inscribed in
In modern geometry (i.e. Hilbert axioms), how do we show that the area of $\triangle ABC$ is less than the area of the sector centered at $A$? Is there a way to show it without calculus or analytic ...
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1answer
23 views
Area between curves is
The area bounded by the parabolas y^2=4x and y^2=x and the lines x=1 and x=4 is
I had tried this and got my answer as 1. But there is no such option. Any help is appreciated.
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Angles between normal vectors vs angles between faces
I am to prove two different formulas, but I don't get how are the values in the formulas different.
This is a tetrahedron problem, specifically angles.
At first, I am supposed to prove
$\ A^2 = B^...
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1answer
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Finding the area of a Paralleltope [on hold]
If $P $ is the paralleltope spanned by $(0, 1, 2)$ and $(3, 4, 5)$ in $\mathbb R^3$, what is the two-dimensional area of $P$?
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$ABC$ is a triangle such that $BC = 74 cm$ and point $D$ is on $BC$ so $BD=14cm$.If $\angle ADB=60^\circ$ then what is the area of triangle $ABC$?
In the figure below, $ABC$ is a triangle such that $\angle BAC = 150^\circ$ , $BC = 74 cm$ and point $D$ is on $BC$ such that $BD=14cm$.If $\angle ADB=60^\circ$,then what is the area, in $cm^2$, of ...
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Calculate area of a projected image
I've been given the following question as a review problem for my upcoming digital image processing midterm. This question isn't going to be graded and to my knowledge, may not appear on the test, ...
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3answers
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Finding the area of the overlap of two quarter-circles in a square
I am trying to find the area in the overlap of two quarter-circles that are in a $10 \times 10$ square, as somewhat-crudely drawn below:
In this problem I was given a square of side length $10$, with ...
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2answers
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$2$-inch squares are cut from the corners of a $10$-inch square. What is the area of the largest square that fits the remaining space?
$2$-inch squares are cut from the corners of this $10$-inch square. What is the area in square inches of the largest square that can be fitted into the remaining black colored space?
I approached ...
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4answers
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Finding the maximum area of a quadrilateral when three points are given
I am working on problems in the chapter "Applications of Derivatives". I encountered the following problem:
Question:
Four points A,B,C, and D lie in that order on the parabola $y=ax^2+bx+c$. ...
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1answer
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$f(x)=\int_{-1}^{x}(1-\left | t \right |)dt(x\geq -1)$,The area of the curve $f(X)$ and x-axis
$$ f(x)=\int_{-1}^{x}(1-\left | t \right |)dt(x\geq -1)$$ ,The area of the curve $f(X)$ and x-axis
When I did the calculations, I used wolfram alpha.It is the use of a digital $1 + \sqrt2 $Look at ...
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1answer
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How would you go about finding the area probability?
A triangle is formed inside a square by joining corner C with the mid points of sides AD and AB. If a point in the square is chosen randomly, what is the probability that the point will be inside the ...
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2answers
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Distance between 2 functions in metric space. Is the area between two curves a distance?
In the study of metric space, I've encountered two kinds of distances between 2 functions:
1)
$\begin{array}{l}{\text { Let } a<b \text { and } X=C([a, b]) \text { be the set of continuous ...
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Area of infinite number of points
Let's say I have a set $S$ of points in $\mathbb{R} ^2$, and I was able to find a bijection from $S$ to the unit disk. Can I say that the area of points in $S$ is $\pi$?
I doubt it.. so my ...
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2answers
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A goat is tied to the corner of a shed
A goat is tied to the corner of a shed 12 feet long and 10 feet wide. If the rope is 15 feet long, over how many square feet can the goat graze ?
I know that this question has already been asked a ...
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2answers
29 views
Tangent Line and area of a triangle
The line tangent to the graph $f(x)=e^x$ at a point $x \le 0$ intersects both axes forming a triangle. Find $x \le 0$ that minimizes the area of this triangle and the value of the corresponding area....
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1answer
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On finding the region closer to the base of an isosceles triangle than the equal sides
The question is posed as follows:
Let $O(0,0), A(2,0), and B(1, \frac1{\sqrt3})$ be the vertices of a triangle. Let $R$ be the region consisting of of all those points $P$ inside $\triangle OAB$ ...
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problem of analytical geometry, find area function
How this problem is solved?
Determine the "t" function that represents the area of the rectangle inscribed within the following graphs
$$f(x)=x^2-4x$$
and
$$g(x)=\frac{4x-x^2}{2}$$
Edit There was ...
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1answer
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The area of the region bounded by $f(y)=y^2$ $g(y)=y+2$
So finding the inverse of the functions gives us
$$f(x)=\sqrt{x},-\sqrt{x}$$
$$g(x)=x-2$$
Having two different outcomes for the $f(x)$ threw me off at first but, after looking at the graph with all ...
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3answers
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calculation of area and perimeter of cleared areas (without using integral calculation)
How can I find the area and perimeter of [these cases], can you help me?
Thanks
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1answer
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Units of the rate of change of the area with respect to a linear measure
Suppose we have:
Find the instantaneous rate of change of the area of a square with respect to its side when the side is $2\,\textrm{cm}$.
Solution.
Let $a$ be the side of the square. Then $A=a^2$...
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3answers
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Find area of shaded regions in a triangle
I am trying to solve this problem.
In $\triangle ABC$, $CD=3BD$ and $DE=AE$. Given that the area of $\triangle ABC$ is 14$cm^2$. Find the total area, in $cm^2$, of the shaded regions.
I divided the ...
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1answer
29 views
Find area bounded by the curves
If $y=f(x)$ is solution of differential equation $ydx+dy= {-e^{x}}{y^2}dy$ with $y(0)=1$
find the area bounded by curves:
$y=e^{x}$,$y=f(x)$&$x=1$
My attempt : since given differential ...
2
votes
2answers
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Proving a formula for the area of a parallelogram from coordinates
I have this simple (high school level) exercise:
The $ABCD$ quadrilateral is a parallelogram of vertices $A(0;0)$, $B(20;10)$ and $D(10,y)$. If your area is $600$, what is the measure of $y$?
I ...
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1answer
37 views
Area of a circle smaller than one?
If a circle has radius less than one, does it mean that the circumference of the circle is bigger than the area? How can that even be possible?
For example, if a circle has radius $0.5$, then the ...
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Distance of chord for given area?
For a circle w/ a unit radius, how far from the center of that circle must the center of a chord be for the area under that chord (the one that would not include the circle's center) to be A?
If $...
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1answer
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Existence of a closed curve with zero area and infinite perimeter, but not conversely
I want to prove that we can find planar simple closed curves with arbitrarily small area and '$infinite$' perimeter, but not the other way around, i.e. we cannot find a simple closed curve with ...
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0answers
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First variation of length
Let $M^3$ be a Riemannian manifold with nonempty boundary and let $\Sigma$ be a smooth surface with boundary. Consider $\Phi : \Sigma \times (-\varepsilon, \varepsilon) \to M$ a proper variation of a ...
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Prove that the area of the trangles are equal.
Prove that the area of all the traingles in the figure below are equal.
I tried using geogebra to determine an arbitrary values of $a$ , $b$, and $c$. I found out that the triangles have equal ...
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Finding the area of the region bounded by $x=0$, $y=0$, $2x^2=\sqrt{x^2+y^2}$, $2y^3=\sqrt{x^2+y^2}$
I have 4 equations and need to find the area bounded by the corresponding curves.
I don't know how to approach it.
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2answers
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Ways to prove the area of an ellipse formula
One can prove the ellipse area formula $A=\pi a b$ ($a$, $b$ the major and minor semi-axis) either by integration or by the stretched-circle argument. See for instance here: https://proofwiki.org/wiki/...
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1answer
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Ratio of surface area of two prisms given only volume of those prisms?
I'm trying to help my son with a math problem that totally has me stumped, and searching online is not helping.
Given two prisms with volume 1536 and 375, what is the ratio of their surface areas?
...
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1answer
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Area of the shaded region- Rotating Wheel
I wanted to compare answer for area of the region in the middle of the square, the leaf sort of shape. So the circle is like a wheel and as it turns to the other side, it basically draws the upper ...
0
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1answer
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integral of chord length divided by surface area of sphere
I'm trying to find the integral of a chord length of a circle, divided by the surface area of a sphere. Imagine a circle, that is stuck between two layers of a spherical shell, and then take discrete ...
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3answers
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What is the area of a region bounded by the curve $y=e^x$ and the lines $y=1$ and $x=1$?
What is the area of a region bounded by the curve $y=e^x$ and the
lines $y=1$ and $x=1$?
When $x=1$, $y=e$. When $y=1$, $x=0$.
I tried to find the area by saying that $A=\int^1_0 e^x dx= e - 1$.
...
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3answers
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Equation of a line that form a triangle of area 8
Find the equation of the line that passes through the intersection of two lines, $\ 3x-4y=0$ and $\ 2x-5y+7=0$, and form a triangle of area 8 with the coordinate axes.
I know that the intersection ...
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1answer
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Is there any difference in definition of Area in maths and physics?
I am a little bit confused after reading the definition of area :
The area of a shape can be measured by comparing the shape to squares
of a fixed size.[2] In the International System of Units (...
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2answers
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Fraction represented by shaded area
What fraction of the area of square with side of length $a$ does the shaded area represent?
I solved the problem of finding the fraction area of the triangle with sides of length $a$, $d$ and $e$; ...
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2answers
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Finding the equation of the ellipse given the area and making a guess about the shape of the ellipse with maximum area
The standard form of the ellipse with the foci on the x-axis
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a+b=20$$
Given the formula for the area of ellipse is
$$A=\pi ab$$
a) How do I find the area of ...
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3answers
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How to prove $I_n = \int_0^{\pi/2} \sin^n(x)dx = \int_0^{\pi/2}\cos^n(x)dx$ without using induction.
$$I_n = \int_0^{\pi/2} \sin^n(x)dx = \int_0^{\pi/2}\cos^n(x)dx$$
I must show the above equation without using induction. I would simply refer to the visuals: area under the curve between 0 and $ \...
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1answer
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painting a wall randomly
Lets say I am trying to paint a wall by randomly (uniform) shooting at it with a paintball gun. On average, how many paintballs will it take so that 99% of it has been covered?
The first paintball is ...
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2answers
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Calculating area of a shape with circular boundaries with elementary methods
Question. $\square ABCD$ is a square with $AB = 10$. Circle $O$ inscribes the $\square ABCD$. The center of the arc is $A$. What is the area of the colored area?
Explanation: This problem can be ...
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Minimum surface of revolution
Let us consider we need to find a curve between $(-x,y)$ to $(x,y)$ such that the surface of revolution of this curve has minimum surface area.
I proceeded to find area by considering the infitesimal ...
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Radius of circle included in a certain area.
Area $A$ is defined as the area of intersection between $x^2+x-2$ and $3x+1$. If a circle $x^2+y^2=r^2$ fits inside the area $A$, then what is the range $0 < r < \dots$?
At first, since it ...
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3answers
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Australian Maths Competition Area Question [closed]
PQRS is a square. T and U are midpoints of the sides PS and PQ
respectively. TQ, SU and PR intersect at V.
This is a question from the 2009 Intermediate Division AMC paper. I was given it in a ...
