Questions tagged [area]

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

Filter by
Sorted by
Tagged with
0
votes
4answers
29 views

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 ...
1
vote
1answer
21 views

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)
-5
votes
0answers
25 views

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 ...
3
votes
1answer
52 views
+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 ...
2
votes
1answer
43 views

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 ...
0
votes
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.
0
votes
0answers
13 views

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^...
1
vote
1answer
23 views

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 $P$?
1
vote
3answers
52 views

$ABC$ 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 ...
-2
votes
1answer
15 views

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, ...
2
votes
3answers
67 views

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 ...
6
votes
2answers
53 views

$2$-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 ...
3
votes
4answers
146 views

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 $y=ax^2+bx+c$. ...
0
votes
1answer
14 views

$f(x)=\int_{-1}^{x}(1-\left | t \right |)dt(x\geq -1)$,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 ...
0
votes
1answer
21 views

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 ...
0
votes
2answers
40 views

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 ...
0
votes
2answers
31 views

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 ...
15
votes
2answers
3k views

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 ...
0
votes
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....
1
vote
1answer
39 views

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 $\triangle OAB$ ...
1
vote
3answers
63 views

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 ...
0
votes
1answer
19 views

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 ...
0
votes
3answers
48 views

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
2
votes
1answer
17 views

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 $A=a^2$...
1
vote
3answers
84 views

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 ...
0
votes
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
58 views

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 ...
-1
votes
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 ...
0
votes
3answers
35 views

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 $...
1
vote
1answer
27 views

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 ...
1
vote
0answers
40 views

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 ...
7
votes
3answers
167 views

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 ...
-1
votes
1answer
33 views

How do I find the area under a wave/quadratic?

The roots A and B are (-1,0) and (2,0) respectively.
0
votes
2answers
34 views

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.
1
vote
2answers
69 views

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/...
0
votes
1answer
36 views

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? ...
0
votes
1answer
28 views

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
votes
1answer
24 views

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 ...
1
vote
3answers
41 views

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 $A=\int^1_0 e^x dx= e - 1$. ...
0
votes
3answers
38 views

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 ...
0
votes
1answer
44 views

Calculus 2 problems help [closed]

Ive been struggling with this problem. Thanks!
2
votes
2answers
50 views

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 (...
1
vote
2answers
58 views

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 $e$; ...
0
votes
2answers
41 views

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 ...
0
votes
3answers
50 views

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 $ \...
1
vote
1answer
47 views

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 ...
4
votes
2answers
91 views

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 ...
0
votes
0answers
26 views

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 ...
-1
votes
2answers
44 views

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 ...
2
votes
3answers
74 views

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 ...