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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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 ...
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 ...