For questions about area of plane figures.

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1answer
51 views

The area visible from two lighthouses with angle of vision 30 degrees, built at distance 10km from each other

The distance between 2 lighthouses is 10 km. What is the maximum area of the ocean in which both can be simultaneously visible if the angle of vision for each lighthouse is 30 degrees?But the minimum? ...
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0answers
44 views

Calculate the area of wiper [on hold]

I was trying to calculate the area of wiper in car. The size of wiper is 34cm. Can anyone help me to solve it? The most problem is in green part. The important thing is the way of solving.The ...
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0answers
12 views

Idea behind shoelace formula

I am trying to get the Idea behind the shoelace formula. I could not find a book where it is explained in detail so I searched the web and could not found a satisfying explanation. Wikipedia says that ...
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1answer
65 views

area-preserving iff $|\det |=+1$

Why is a (not necessarily linear) mapping $f:\mathbb{R}^n\rightarrow \mathbb{R}^n$ area- and orientation preserving iff the determinant of its jacobian is $\pm 1$ ? (I understand by an ...
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0answers
30 views

What is the probability of shooting a puck overlapping the boundaries to get a prize?

Hello, I am new to the forum, and the maths teacher just asked the whole class this question about probability and all of us can't answer it. The question is: there are 9 grid squares on the table, ...
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2answers
63 views

Calculus exam question logic help? [on hold]

We had an exam of Calculus few days ago and that is the assignment we were given, and I don't know how to solve it.Could you please help me with it? Thanks. Like good gardeners, we would like to ...
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4answers
77 views

Area Ratio of a Polygon

Let $A_{1}A_{2}A_{3}A_{4}A_{5}$ be a regular pentagon with side length $1$. The sides of the pentagon are extended to form the $10$-sided polygon shown in bold at right. Find the ratio of the area ...
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27 views

Math surface question which I don't know how to solve

We would like to build a fence around our garden with 3000m available. We would like to have a rectangular fencing, which is divided on three unequal parts. What is the biggest area, that we can ...
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1answer
16 views

Triangle Area Ratio Theorem Problems?

Having a hell of a lot of issues with these problems, supposed to be on the topic of triangle area ratio theorem (ratio area of triangles = ratio of triangles' heights x ratio of triangles' bases.) ...
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2answers
32 views

Find the area between these two functions using integration

The functions are $$ f(x) = \ln (x) $$ $$ g(x) =(\ln(x))^2 $$ Is there a simple way of finding area other than using the long method of integration by parts
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1answer
9 views

Area with different unit measurements

What is the area of a rectangle, in square meters, with a length of 108 meters and a width of 300 millimeters? I think it could be 324 sqm.
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1answer
33 views

Area of shaded region to the square

In this question, I was able to make out that root(2) * EF = 1/2 AD. Then area of the small square = root(2) EF = 1/2 AD => ...
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1answer
12 views

Find the area enclosed by curve with polar coordinates

I am having a little difficulty finding the area enclosed by the curve, $r(\theta) = 4 + sin\theta + cos\theta$ with $0 \le \theta \le 2\pi$. I tried integrating over $0 \le \theta \le 2\pi$ and $0 ...
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0answers
28 views

Get the area of a “circle section”

Well given the curve that follows the following circle, and has end points as specified: $$(x +0.804)^2 + (y - 0.434)^2 = 3^2$$ $$P1 = (0.75, 3)$$ $$P2 = (2, 1.5)$$ I need to calculate the area of ...
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2answers
38 views

Optimization problem of two variable

Find two numbers $a$ and $b$ with $a \leq b$ such that $\int_a^b (6-x-x^2)dx$ has the largest value.
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0answers
21 views

Equiareal Voronoi tessellation

I'm interested in even (or "proportional") disrtributions of points on 2D areas. Here is the initial question, but many others ideas appeared later. Centroidal Voronoi tessellation is well known ...
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0answers
13 views

General formula for n-Simplex side-lenghts given n-volume and angles

Given a flat triangle's three angles $\phi_i $, and its area $A$, you can calculate the $i$th sidelenght $s_i$ (using Einstein's sum-convention) like so: $$ s_i=\frac{\sqrt{2A} \sin \left(\phi ...
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1answer
41 views

Calculating area of complex ploygons (odd shapes)

We need a formula / algorithm to find the area of a shape, based on user selected co-ordinates (mouse click). We know the x and y co-ordinates of each line drawn by the user, then using the pixel ...
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2answers
17 views

Finding the weight of a solid cylinder.

Find the weight of a solid cylinder of radius 10.5 cm and height 60 cm if the material of the cylinder weighs 5 g per $cm^3$. What Ive tried: Radius=10.5 cm Height=60 cm Weight of material=5 g per ...
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2answers
78 views

Why is the volume one third of that? I mean, where's the fault in my logic? [duplicate]

The volume of a cuboid is $l \times b \times h$. That is, it is equal to base area times height. I think it means that the base is added up height times, it becomes volume (It makes sense if we think ...
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2answers
25 views

How does the circumference of the top + bottom sides of a cylinder effect our calculations when working out the surface area?

I was watching a video tutorial on khan academy, (I've included the link at the bottom), and the question states that there is a 8cm cylinder, with a radius of 4. Part of the video shows a worked ...
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2answers
35 views

Finding the area of a triangle, given the distance between center of incircle and circumscribed circle

Consider the following depiction: $ABC$ is an isosceles triangle ($AB=AC$), where the two angles opposite the equal sides are equal $\beta$ ($\beta>60$), and $AD$ perpendicular to $BC$. $O$ is ...
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0answers
35 views

Evaluating the divergence theorem for region above $z=0$, below $z=x$ and inside $x^2+y^2=1$ where $\hat F=(xz,yz,z^2)$

Can someone please confirm my working below: The answer am getting look kinda crazy -Thanks. $$\color{green}{\hat F=(xz,yz,z^2)}$$ $1.$For the surface where $\color{green}{z=0}$ i.e. (flat ...
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0answers
55 views

Largest rectangle bounded under a function

Let $f$ be a positive monotonically increasing real function in $[0,1]$. Let $F$ be the area under the curve of $f$ ($F=\int_0^1{f(x)dx}$) For every $x\in[0,1]$, let $G(x)=f(x)*(1-x)$ = the area of a ...
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1answer
55 views

Finding the surface area $\iint_{s} f \, dS$ of $z=x^2-y^2$ cut off by $z=4-2y^2$

Finding the surface area $\iint_{s} f \, dS$ of $z=x^2-y^2$ cut off by $z=4-2y^2$ I have no idea which parametrization to use for this, however i did figure out the following: I think the ...
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1answer
38 views

Finding the surface area $\int \int_{s} f \, dS$ of $z=\sqrt{x^2+y^2}$ lying inside $x^2+y^2=x$

$z=\sqrt{x^2+y^2}$ is the surface we working on. I am a bit stuck on choosing the limits for this problem, I have done the following: ...
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0answers
37 views

Find the area and perimeter of a self-intersecting polygon using out of order coordinate points.

I was wondering if there was any algorithm or approach to find the perimeter and more importantly the area of a self-intersecting polygon using an array coordinate points. The problem is that ...
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5answers
79 views

Area of triangle with given coordinates of the vertices

The question for my math is: "Sharon made a scale drawing of a triangular park. The coordinate for the vertices of the park are: $(-10,5)$, $(15,5)$, $(10,12)$. What is the area of the triangular ...
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2answers
40 views

How to find the inradius of a triangle with given side lengths?

I need to find the inradius of a triangle with side lengths of $20$, $26$, and $24$. I know the semiperimeter is $35$, but how do I find the area without knowing the height? Thank you.
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1answer
32 views

What is the ratio of areas of quadrilaterals ABFE and EFCD??

$ABCD$ is a trapezium with parallel sides $AB = a$ and $DC = b$. If E and F are mid-points of nonparallel sides AD and BC respectively, then what is the ratio of areas of quadrilaterals $ABFE$ and ...
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3answers
115 views

The area of intersection of an isosceles triangle with another triangle

I tried graphing the equations that form the two isosceles triangles and integrating the bounded area and got 7.456 as my answer after rounding. The answer key has the answer listed as 7.2 However, ...
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1answer
32 views

Find the area of a subset of $\mathbb{R}^3$ given by an implicit relation.

Let x, y, z be real numbers and let $A = \begin{bmatrix} 1&x&x^{2} \\ 1&y&y^{2} \\ 1&z&z^{2} \end{bmatrix} $ Let S be the subset of $\mathbf{R}^{3}$ given by $S = \{ ...
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0answers
31 views

Sum of all n dimensional spheres?

I was messing around and made some code to find the area of an n dimensional sphere. I noticed that as n increases, the area tends towards zero. These were the results: ...
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1answer
55 views

How to calculate the area between $y=e^{-x}$, $y=x$ and $x=0$

My problem is that little point that comes from the equation $$e^{-x} = x$$ I can't solve that one. Is there another way without knowing that point or a way to calculate it? Thanks in advance!
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1answer
25 views

How to find the integration bounds when calculating area

To calculate an area between curves, I need to integrate with respect to x between the curve $y=\sqrt{2x}$, the x-axis and the line $y=\frac{4x-12}{5}$ My understanding, using google to display plot ...
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0answers
27 views

Surface area of cylindrical surface using double integrals

The formula for the surface area of a cylindrical surface is given by the equation $$A(S) = \iint_D \sqrt{1 + \left(\frac{\partial z}{\partial x}\right)^2 + \left(\frac{\partial z}{\partial ...
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1answer
45 views

Inequality between area and boundary length, $4\pi A \leq L^2 $

Suppose we have a simply connected region $R$ in $\mathbb{R}^2$ with area $A$ and the boundary of $R$ is a curve sufficiently well behaved (say piecewise $C^1$) that we can say it has length $L$. Then ...
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1answer
45 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
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1answer
33 views

ACDF (labelled clockwise) is a square of unit length. B is the midpoint of AC. E lies on FD such that FE = 1/4 and ED = 3/4. Find the area of BHEG.

I have solved this problem by use of the Cartesian plane, but the solution is long and I am sure that I have overkilled it and that there is a simpler solution... Based on where this question came ...
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1answer
47 views

Evaluate integral by interpreting it in terms of areas

I tried (a) and I got 5, but I am suppose to get a 4. I really need a good explanation to understand how to approach these problems. I tried searching in youtube and stuff, but it was not helpful. ...
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2answers
463 views

$\pi$ in terms of $4$?

I'm trying to define $\pi$ in terms of $4$ by placing a unit circle inside a square, and subtracting the corners of the square. I'm attempting to use summation to define the area of a corner, then ...
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1answer
25 views

Elementary question: Integral of area function

I am sorry for this elementary question. I have searched a bit but haven't found what I am looking for precisely. I am trying to determine how to the volume of liquid in an irregularly shaped ...
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2answers
44 views

Prove that $\frac{1}{2}ab \equiv \int_0^b \! f(x) \, \mathrm{d}x$ when calculating the area of a right triangle.

Triangle $ABC$ is a right triangle with sides $AB$, $BC$ and $AC$. $a$ is the length of $AB$. $b$ is the length of $BC$. $c$ is the length of $AC$. If $a = 3$, and $b = 4$, we can use ...
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1answer
33 views

Find the area of the region enclosed by the curves in the first quadrant

Find the area of the region enclosed by the curves $y=3x^2$, $y=8x^2$, $4x+y=4$ in the first quadrant Do you start by finding the boundaries?
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1answer
33 views

Area of a region bounded by $y=\sqrt{|x|}$ and $5y = x+6$

Find the area of the region bounded by $y=\sqrt{|x|}$ and $5y = x+6$ by looking at where the curves intersected on a graph I got $$\int_{-1}^4\Bigg[\frac{x+6}{5} - \sqrt{|x|}\Bigg]\,\, dx + \int_4^9 ...
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0answers
38 views

How to calculate the height of a segment based on radius and area

I'd like to calculate the height of a segment based on the area. I have the radius of the circle, the area of the segment and need to calculate the height of the segment. I found the following ...
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1answer
31 views

How is the area of this triangle calculated

I was reading "Problems of Calculus in one variable" by I A MARON, and came across this solved example in first chapter which I am unable to comprehend, please help me understand this. Scan of the ...
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1answer
28 views

Area of ellipse formed by slicing a cylinder

What is the equation of the area of the ellipse when a cylinder of radius x is cut by a plane inclined at an angle a. Angle a is the angle between the plane and the axis of the cylinder. If a is 90 ...
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2answers
39 views

Find the area of a shaded region

I'm trying to teach myself some elements of calculus in preparation for my class next semester, but I'm not sure how to work this problem. I've always had trouble dealing with areas inside of shapes. ...
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1answer
16 views

Area of a Parallelogram Using Vectors

I am not sure if I am doing this problem correctly. I need to find the area of the parallelogram whose vertices are the points $P(0,1,1), Q(1,2,1), R(2,4,1), S(3,5,1)$ So to find the area I need to ...