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

learn more… | top users | synonyms

-1
votes
3answers
20 views

Area bound by two curves. [on hold]

What is the area of the region bounded by the curves $y= 2x^2+7x$ and $y= 2/x$ between $x= 1$ and $x= 3$? Thank you!
0
votes
2answers
26 views

Co-ordinate geometry and area of triangle

When a straight line $ax+by+c=0$ forms a triangle with the axes $x$ and $y$, what is the general formula for the area of the triangle?
3
votes
0answers
22 views

Minimizing Area by Approximation

Suppose I have an increasing step function $E_c$ given by $$E_c(\phi) = \sum_{i=1}^n E_i \theta(\phi - \phi_i),$$ where $\theta$ is the Heaviside step function and $E_i$, $\phi$, and $\phi_i$ are all ...
0
votes
1answer
34 views

How many square millimetres are in 0.000075 square metres?

Doing my head in a bit.. $0.000 075 \times 100$ = in square cm, and times that by $10 =$ square mm but apparently I'm off by a couple of orders of magnitude.
2
votes
1answer
58 views

Find the area bounded between $f(x)=\frac{\arctan(x)}{x^2}$ and $g(x)=\frac{\arctan(x)}{x^2+1}$

Find the area bounded between $$f(x)=\frac{\arctan(x)}{x^2} \quad\text{and}\quad g(x)=\frac{\arctan(x)}{x^2+1}.$$ The title says the question. The limits are from 1 to infinity. I know that I ...
6
votes
1answer
44 views

How to calculate the area of a region with a closed plane curve boundary?

Under the conditions of Green’s Theorem, the area of a region $R$ enclosed by a curve $C$ is $$\oint_C x \, dy=-\oint_C y \, dx=\frac{1}{2}\oint_C (x \, dy - y \, dx)$$ I tried to use the result to ...
0
votes
1answer
47 views

Minimal area of triangle

We have the points $A(2, 3-m), B(m+2, -1)$ and $C(m, 2-m)$. Where $m$ is a real number. Find $m$ for which the area of triangle $ABC$ is minimal. So I've tried to find the equation of line $BC$(the ...
2
votes
2answers
40 views

How to calculate the area of a parabolic dish

I feel like this should be really easy, but I'm not sure if I'm doing it correctly so I'm going to give it a go here, and if I'm not very good at maths (I'm not) then you can hopefully correct me! ...
13
votes
6answers
2k views

How is the area of a circle calculated using basic mathematics?

Area of a circle is addition of circumference of layers of a onion. If n is radius of a onion then area is $$ A = 2 \pi \cdot 1 + 2 \pi \cdot 2 + 2\pi \cdot 3 + \ldots + 2 \pi \cdot n $$ which $$ ...
-2
votes
3answers
87 views

Circles in circle

If we are given one big circle and infinite amount of smaller circles with equal radius (of course radius of the smaller is < radius of the big one) and we have to put in the center of the big ...
2
votes
1answer
48 views

Uniqueness of a number $area(A)$

I have the following definition of area: Let $A$ be a bounded set from $\mathbb{R}^2$. We say that $A$ has area if there exist two sequences $(E_n)_{n\in \mathbb{N}}, (F_n)_{n\in \mathbb{N}}$ of ...
0
votes
0answers
22 views

Finding area by integration, increasing inaccuracies with complex functions?

I am looking for an explanation as to why the method of integration to find the area of function using limits provides a greater % difference between other methods (In this example Simpsons) with ...
0
votes
0answers
22 views

How can I find how many cubic cm is one piece of lath? [closed]

Assuming it has dimensions: 1.3 cm thick, 7.4 cm width and 120 cm length...
-1
votes
1answer
35 views

Find the area of the region of the XY -plane enclosed by the given curve with logarithm [closed]

First of all let me thank one and all for helping in prev problem, and now: Find the area of the region of the XY-plane enclosed by the curve $$y=\frac{lnx}{x}$$the line $x=e$ and the $x -axis$. My ...
0
votes
1answer
54 views

Finding the area between $x \sqrt{4x-x^2}$ and $\sqrt{4x-x^2}$

So I've been doing real analysis for a last couple of days, and stumbled upon this task. The task is to find the area enclosed by $$y_1=x\sqrt{4x-x^2} $$ and $$y_2= \sqrt{4x-x^2} $$ This is one of ...
4
votes
2answers
103 views

Surface area of the ellipsoid $\frac{x^2}{16}+\frac{y^2}{8}+z^2=1$

My professor gave us this question on a calculus II quiz. One of my calculus III pals suggested I use surface integrals, but that tool is not available to us (I don't know how to use it yet, nor do my ...
0
votes
0answers
21 views

Help with Apostol's “Calculus, vol. 1”, Section 1.18

In section 1.18 ("The area of an ordinate set expressed as an integral"), Apostol proves two theorems. the first, theorem 1.10, deals with the area of a function's ordinate set; the second, theorem ...
0
votes
1answer
34 views

Straight Lines; The area enclosed by |x| +|y| =1 [closed]

Find the area enclosed by the following graph : $|x| +|y|=1 $
1
vote
2answers
47 views

Mandelbrot Set area

If there are an infinite amount of details that can be found in a Mandelbrot set, shouldn't the Mandelbrot Set have an infinite area? Supposedly the area of a Mandelbrot set is 1.5065918849 ± ...
0
votes
1answer
28 views

Snowflake-sequences - Area - Circumference

Consider the following inductively defined snowflakes-sequences: $S_1$ is an equilateral triangle with edge length $l_0$, and $S_{n+1}$ emerges from $S_n$ by dividing each edge by 3 and the middle ...
4
votes
2answers
177 views

Finding the area remaining after flipping a rectangle inside a rectangle

Let $r$ be the inside rectangle of base $b$ and height $h$. Let $R$ be the outside rectangle of base $B$ and height $H$ The dimensions of $r$ and $R$ are related in the following way: I want to ...
1
vote
2answers
17 views

Surface area of revolution for curves symmetrical on the axis of revolution.

I understand that surface area generated when an curve is rotated on the x axis by 2Pi radians is given by: 2Pi∫yds How is this area affected when the object is symmetrical on the x-axis, e.g. an ...
0
votes
1answer
49 views

Math Problem Help || Trig (Updated picture) [closed]

So I got the following math problem I solved but I'm not confident with my answer. My answer was 32. The question is to find the area of the following: ...
1
vote
4answers
45 views

Compute the area of specific shapes [closed]

I'm trying to calculate the dashed area in the following pictures, and I can't solve them. I tried to guess the areas, subtract some shapes from others, but I'm confused if I calculated them wrong or ...
1
vote
0answers
53 views

Calculating the Area of a Circle Occupied by a Rectangle

This is a question regarding how to calculate the area of a circle occupied by a rectangle when that rectangle is larger than the circle (see this link for a example image ...
4
votes
5answers
143 views

What fraction of a sphere can an external observer see?

Here is a geometry problem. Let there be a ball of radius R and let's call it the Moon. Let there be an external observer: A. A is at a distance d to (the surface of) the Moon. [Edit] A is a ...
0
votes
1answer
31 views

Points in a given volume/Area

I have a rectangular prism(3D bounding box) for which i have the point(i.e center of gravity) and the height,width,depth dimensions . Given these parameters, is it possible to find all the points that ...
1
vote
1answer
25 views

Formula for area in a special occasion in polar coordinates.

I know that the area of a curve given in polar coordinates is $$\int_{\theta_1}^{\theta_2}\frac{r^2}{2}d\theta$$. But what is the area outside one curve and inside another, when one of them is not ...
2
votes
1answer
60 views

Need Help Finding Area of A Rectangle

I am really not sure if this is the right place to post a question like this, but I'm absolute stuck on this question. I would appreciate an answer greatly. A park is undergoing renovations to its ...
2
votes
3answers
43 views

Find the area of the region between two lines and $ x = 0$

I need to know the area between $y = 2x+4$ and $y = 4x$. Between each other before they intercept at $(2, 8)$. That's against the $y$-axis. this will help
0
votes
1answer
26 views

Find a volume of a figure given by an astroid rotating around an axis

In the class we were given a task to find a volume of a figure of revolution. The figure is an astroid $x=a\cos^3{t}, y=a\sin^3{t}$ axis is $x=a$. And I thought that instead of doing integration (wich ...
1
vote
1answer
69 views

Intersection of a convex polygon and a moving circle

I have a straight line which intersects a convex polygon in 2D plane. There exists a circle with constant radius. The center of circle is moving on this line. So at first the polygon and circle don't ...
0
votes
0answers
23 views

Given verticies find the area of the triangle formed

When I looked at this problem I didn't think it seemed all that hard until I actually tried it. The problem is this: Given the rectangular vertices $O(0, 0, 0), P(-1, 2, -3), Q(-2, 3, -4), R(0, 0, ...
2
votes
3answers
272 views

Infinite points on a paper?

I remember solving questions like this: On a paper with dimensions $30cm$ x $21cm$ if a rubber (erasers)* is dropped, what is the probability that it falls over a grey shaded region of dimensions ...
1
vote
2answers
33 views

Surface area of a torus

One can generate a torus as follows: $\vec{g}=((b+a\cos u)\cos v, (b+a\cos u)\sin v, a \sin u)$. To find its area, we can use a surface integral of the form $S=\int\int_{D_{uv}} {\lVert \frac{∂g}{∂u} ...
3
votes
2answers
49 views

Expected value of area of triangle

Here is the problem: Let $A$ be the point with coordinates $(1, 0)$ in $\mathbb R ^2$. Another point $B$ is chosen randomly over the unit circle. What is then the expected value of the area of the ...
0
votes
1answer
83 views

Area of Circle Overlapped by Rectangle

I'm trying to determine 'how much' (as a percentage) a 2D rectangle fills a 2D circle. Actual Application: I was comparing the accuracy of some computer game weapons by calculating the max possible ...
3
votes
1answer
54 views

Bergman space. What is area measure?

I have read that the Bergman space $A^p(\Omega)$ consist of all the analytic functions $f$ in $\Omega$, such that $$ \left( \int_{\Omega} |f(z)|^p dA \right)^{1/p} < \infty $$ where $dA$ is the ...
1
vote
3answers
39 views

Modeling the relationship between perimeter and area

Is there any equation that models the relationship between the area and perimeter of a rectangle?
4
votes
2answers
228 views

Maximum area of a fenced playpen on the side of a house.

Here's an interesting problem: you just got a really cute puppy, and you want it to have a large rectangular playpen to run around in. What's more, your neighbor just happened to have 100 feet of ...
1
vote
1answer
29 views

Inequalities solved by considering areas

So basically, I've figured out the first two parts of the question, and I really need help with part b. I'm not sure how to tackle the question, nor where to begin. Can anyone help me? Please. All ...
2
votes
0answers
40 views

Finding area of a spheroid

Let $M=\{(x,y,z)\in \Bbb{R}^3 : (x/a)^2 + (y/b)^2 + (z/c)^2 = 1\}$. Find $\text{vol}_2(M) = \int_M 1 dS$. My attempt: The map $$\Phi:(0,\pi)\times (0,2\pi)\to \Bbb{R}^3\\ \qquad (\varphi, ...
1
vote
2answers
61 views

Area between a semicircle and a 45° line

I'm studying for a Calculus test and I met the following question: There's a semicircle $$y=\sqrt{1-x^2}$$ and a line at 45° degrees v=x. The task was to find the area in the positive quadrant. I ...
0
votes
0answers
21 views

Highest area rectangle in a rectangle trapezoid

There is a rectangle trapezoid with base sizes 8 and 24 and height of 12. Is there a way of finding highest area rectangle inside a trapezoid which 2 points would be in sides of a trapezoid? I ...
9
votes
6answers
529 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
0
votes
0answers
24 views

The area of a stereographic projection

I'm newbie at multidimensional integration and I'm trying to make a working algorithm in Wolfram that can help me compute the areas on the unit sphere without complicated parametrization, provided I ...
2
votes
2answers
83 views

Curve fitting the cross sectional area of a cake.

For my final Calculus project I have to find the area of a Bundt cake through the use of cross sectional areas. (Cakeulus) While most seniors in High School who run into this popular calculus project ...
4
votes
0answers
56 views

Are closed simple curves with that property necessarily circles?

This is a more interesting follow-up to the question Are closed simple curves with this property necessarily circles? Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple $C^1$ convex curve and ...
2
votes
1answer
53 views

Are closed simple curves with this property necessarily circles?

Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple curve and $\Gamma$ be the region enclosed by $\gamma$. Let $O$ be the center of mass of $\Gamma$. Suppose that any line that goes through ...
0
votes
0answers
21 views

Given a set of points, find the plane parallel to plane $p$ where your plane cuts the area in half.

Given a set of point $G=\{(x,y,z) | 0 \le x\le2, 0 \le y \le 2, 0 \le z \le xy\}$ for all $x,y>0$ Find the plane $p$ parallel to plane $zy$ whereas you get two areas equal in size What I did was ...