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

learn more… | top users | synonyms

1
vote
1answer
21 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 ...
1
vote
1answer
22 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 ...
0
votes
0answers
13 views

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 ...
0
votes
2answers
37 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 ...
1
vote
2answers
58 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 ...
0
votes
0answers
16 views

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 ...
4
votes
1answer
21 views

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 ...
-4
votes
0answers
52 views

Isoperimetric hexagon and triangle ; comparing their areas. [closed]

A regular hexagon ( all sides of equal length and all angles equal ) and an equilateral triangle is equal circumference. What percent larger is the largest area ??
0
votes
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 $9p^2\ge 12\sqrt{3}\Delta.$ ...
2
votes
1answer
22 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 ...
2
votes
2answers
106 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, ...
1
vote
1answer
15 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?
0
votes
0answers
20 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. ...
0
votes
1answer
26 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 ...
1
vote
0answers
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 ...
7
votes
3answers
64 views

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 ...
1
vote
1answer
33 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 ...
1
vote
3answers
42 views

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 ...
1
vote
1answer
34 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?
-1
votes
3answers
32 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
0
votes
0answers
20 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) ...
0
votes
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 ...
0
votes
1answer
49 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 ...
0
votes
0answers
56 views

What is “Squaring the Circle”

I am unclear about what "Squaring the Circle" is, let alone how people tried to solve it. Please tell me if "Squaring the Circle" means finding square and circle with same area OR finding square and ...
1
vote
1answer
37 views

Find the area bounded by $r=6\sin(2\theta)$

Winplot plot: I tried this: $$A = 4 \cdot \frac 1 2 \int_0^{\pi/2} (6\sin(2\theta))^2 d\theta$$ Is that right? How about $$A = 8 \cdot \frac 1 2 \int_0^{\pi/4} (6\sin(2\theta))^2 d\theta$$
0
votes
1answer
24 views

Find the area inside $r=2+2\sin(\theta)$ but outside $r=4\sin(\theta)$.

Winplot plot: I tried this: $$A = 2 \frac 1 2 \int_0^{\pi/2} (2+2\sin(\theta))^2 - (4\sin(\theta))^2 d\theta + 2 \frac 1 2 \int_{\pi}^{3\pi/2} (2+2\sin(\theta))^2 d\theta$$ Is that right? How ...
0
votes
1answer
11 views

Sum of the length of the perpendiculars - property of equliateral triangles

Consider an equilateral triangle ABC P is a point on AB, Q is a point on BC Suppose we draw perpendiculars from P to other sides. Let s1 be the sum of the length of these ...
-1
votes
1answer
30 views

area and volume [closed]

The total length of all 12 sides of a rectangular box is 60. (i) Write the possible values of the volume of the box. Your answer should be an interval. Now suppose in addition that the surface area of ...
4
votes
3answers
69 views

Why is $f(4)$ the area under $f'(x)$ specifically from $0$ to $4$ and not for ex from $1$ to $4$ or $2$ to $4$?

I've seen the geometric argument for why any differentiable function $f(x)$ gives the rate of change of the area under its own curve to $x$ for a specific input $x$, and it makes sense to me. It also ...
-2
votes
2answers
33 views

Area of polygon inscribed in a circle [closed]

Let $A_n =$ the area of a regular $n$-sided polygon inscribed in a circle of radius $1$ (i.e., vertices of this regular $n$-sided polygon lie on a circle of radius $1$). ($i$) Find $A_{12}$. ...
2
votes
1answer
65 views

Area of Convex hull

For every point set $A \subset R^2$, prove that in general the sum of the coordinates of $\phi(T)$ is independent of a triangulation T and is associated to the area of the Convexv_Hull(A). We ...
0
votes
0answers
17 views

Covering a curve with lattice squares

I am reading a book on analysis in which a curve on a plane is defined to have zero area if for every positive $\varepsilon > 0$ it can be covered with a finite union of rectangles with sides ...
0
votes
1answer
63 views

Find the area inside the lemniscate $r^2 = 8 cos 2\theta$ and outside the circle $r = 2$.

Fooplot graph: I think the formula is $$A = \frac 1 2 \int_{\alpha}^{\beta} (\text{outer})^2 - (\text{inner})^2 d\theta$$ where $\alpha, \beta$ are where they intersect in $[0, 2\pi]$. This ...
0
votes
0answers
27 views

Find the area inside the circle $r = 10 \sin \theta$ and above the line $r = 2 \csc \theta$.

Fooplot graph: I think the formula is $$A = \frac 1 2 \int_{\alpha}^{\beta} (\text{outer})^2 - (\text{inner})^2 d\theta$$ where $\alpha, \beta$ are where they intersect in $[0, 2\pi]$. This ...
0
votes
0answers
24 views

Find the area common to the inside of the cardioid $r = 1+\sin \theta$ and the outside of the cardioid $r = 1 + \cos \theta$.

Fooplot graph: I think the formula is $$A = \frac 1 2 \int_{\alpha}^{\beta} (\text{outer})^2 - (\text{inner})^2 d\theta$$ where $\alpha, \beta$ are where they intersect in $[0, 2\pi]$. This ...
0
votes
1answer
40 views

Find the area of the small loop of the limacon $r = 1+2\cos(\theta)$

Find the area of the small loop of the limacon (graph): $$r = 1+2\cos(\theta)$$ What I tried: Set $r=0$ to get $\theta = 2\pi/3, 4\pi/3$. Then $$A = \frac 1 2 \int_{2\pi/3}^{4\pi/3} r^2 ...
3
votes
1answer
34 views

Find the area of the square using co-ordinates

Given a square $ABCD$ such that the vertex $A$ is on the $x$-axis and the vertex $B$ is on the $y$-axis. The coordinates of vertex $C$ are $(u,v)$. Find the area of square in terms of $u$ and $v$ ...
0
votes
0answers
28 views

Area of a triangle on an Argand diagram

I am working on two problems: 1) Find three distinct roots of the equation $8z^3 + 27 = 0$ I solved this and ended up with \begin{align*}z_1 &= \frac32 \left( \cos (\pi/3) + ...
0
votes
0answers
33 views

Check if n*m area can be filled with a*b sized tiles and find the remainder [duplicate]

How can I mathematically check if $n\times m$ area can be filled with pieces with $a \times b$ area and find the remainder? For example, can $6\times 6$ area be filled with $1 \times4$ tiles? My made ...
-2
votes
0answers
19 views

Calc 3 Surface area of a circle question

I have a calc 3 problem I'm not sure where to begin with this problem. There is an equation of a surface $S$ which is $f(x,y)$, where $x^2 + y^2 <= R^2$, and $|f^x|<=1$ and $|f^y|<=1$. What ...
6
votes
2answers
75 views

Area of greatest integer function

Question: Find the area enclosed by the function: $$\left\lfloor\frac{\left|3x + 4y\right|}{5}\right\rfloor + \left\lfloor\frac{\left|4x - 3y\right|}{5}\right\rfloor = 3$$ where ...
4
votes
2answers
54 views

Possible alternative for finding the Area under the floor function (aka, the integral of floor(x))

So, I had to ask myself the question as to what the area under the floor function could possibly be. I started by graphing the basic $\mbox{floor}(x)$ function (I personally use desmos.com for a nice ...
2
votes
1answer
37 views

Integrating $ \frac{\int_{-\pi}^{\pi} \cos^2(x)|\cos(x)| |\sin(x)| dx }{\int_{-\pi}^{\pi} \cos^2(x)|\cos(x)| dx } $

I'm trying to integrate $ \frac{\int_{-\pi}^{\pi} \cos^2(x)|\cos(x)| |\sin(x)| dx }{\int_{-\pi}^{\pi} \cos^2(x)|\cos(x)| dx } $ I understand that $|\cos(x)|$ and $|\sin(x)|$ when integrated over $- ...
0
votes
3answers
48 views

Find area of shaded area in curve with range of values for $y$

The parabola in the diagram has equation $y = 32 - 2x^2$ The shaded area lies between the lines $y=14$ and $y=24$ Looking at the graph, I only need to find half the area and multiply by ...
2
votes
1answer
33 views

Prove surface area of a sphere using solid of revolution surface area formula.

I have to prove the surface area of a sphere with $r=1$ using the solids of revolution through revolution abouth both the $x$ and the $y$ axis. The formulas are easy. From top to bottom, surface area ...
1
vote
0answers
34 views

The area of trapezium is given by $A=(a^2-x^2)(x+a)$. Find x for the area to be a maximum and find A max.

For the diagram, the area of trapezium is given by $A=(a^2-x^2)(x+a)$. Find $x$ for the area to be a maximum and find $A$ max. Hi, I'm not sure how should i do this question. Can anyone help me with ...
23
votes
3answers
3k views

Where does the gap come from? [duplicate]

Can anyone tell me please where does the gap come from? Thanks and sorry if the question is not exactly relevant, I just didn't know where else to ask.
-1
votes
1answer
31 views

How to calculate top base area with bottom base area and height of frustum?

I have the following frustum The bottom base area $A_1$ is known, the top base area $A_2$ is unknown. We know this about the frustum We know the height $h$ and the angle $a$ of the frustum. Can ...
0
votes
2answers
40 views

question about integration of symmetrical graph to find area

let's say, we have an symmetrical curve such as $x=\sqrt{y}$ If we integrate from 4 to 0, wouldn't it cancel out with the area on the other side of the axis? When integration is performed from 4 ...
0
votes
1answer
27 views

Double integral of off centre circle.

I have the vector field $F = (3xy,-x)$ along the circle $c$ (counter clockwise) which has a radius $a$ and centre $(a,0)$. I want to try and apply Green's Theorem to this, where I obtain $\int\int(-1 ...