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

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Find the value of $f(0)$, where $F'(a)+2$ is the area bounded by…

Question: Let $$F(x)=\int_{x}^{x^2+\frac{\pi}{6}}2\cos^2tdt$$ for all $x\ \epsilon \ \mathbb {R}$ and $f:[0,\frac12]\to[0,\infty)$ be a continuous function. For $a \ \epsilon \ [0,\frac12],$ if ...
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1answer
28 views

solving the area using both axis

Consider a region between the 2 following equations... $x= (y-3)^2 + 3$ and $y= -x^2+5$ bounded by the horizontal lines $y=5$ and $y= -1$. Set up the integral using the y-axis and then set up an ...
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2answers
50 views

Calculate double integral $\iint_A \sin (x+y) dxdy$

Calculate double integral $$\iint_A \sin (x+y) dxdy$$ where: $$A=\{ \left(x,y \right)\in \mathbb{R}^2: 0 \le x \le \pi, 0 \le y \le \pi\}$$ How to calculate that? $x+y$ in sin is confusing as i do not ...
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1answer
39 views

Finding area between curves [closed]

A) Find area between $x^3-15x^2+50x$ and $-x^3+15x^2-50x$. B) Decide whether to integrate with respect to x or y. Then find the area of the region. $y=1/x, y=1/x^2, x=7$ C)" " $x+y^2=2 , x+y=0$ D)" ...
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0answers
31 views

Calculate the area of a solid of revolution

So the subject title is self-descriptive. My question is how can I calculate the area of a solid of revolution with the information below: ...
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0answers
10 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
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12 views

Get area from an ease function

How do i go about finding the area from a ease function, for example Cubic easeOut, examples can be found here: http://robertpenner.com/easing/easing_demo.html i would like to get the area from a ...
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5 views

Get LWH with volume ≥ X and smallest possible surface area

The formula for volume of a rectangular prism is $l\cdot w\cdot h$, and surface area is $2(wl + hl + wh)$. If I already have the volume (ie 20m²) as $X$, what are the optimal values for $l$, $w$, and ...
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1answer
33 views

Surface area of circle extracted from a tube wall

I have made a hollow tube (thickness $1$mm) having inner radius $89$ mm and outer radius $90$ mm (length $400$ mm, can be higher). then I made a circular (circle radius $25$ mm) cut perpendicular to ...
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23 views

Find the maximum volume of the pyramid bounded by the plane and the coordinate planes?

Surface $\sqrt{c}=\sqrt{x}+\sqrt{y}+\sqrt{z}$ , $(c>0)$ I found that at $(x_{0},y_{0},z_{0})$ a tangent plane to the surface is : ...
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2answers
15 views

Formula to find the area in relation to changing lengths of a square

If you double the side length of a square, how many times bigger is the area of the square? How many times bigger is the area if you triple the side length? What about if the side length is ten times ...
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3answers
40 views

Triangle area inequalities

I've got stuck on this problem : Proof that for every triangle of sides $a$, $b$ and $c$ and area $S$, the following inequalities are true : $4S \le a^2 + b^2$ $4S \le b^2 + c^2$ ...
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1answer
32 views

$S \leq \frac{(a+b)(c+d)}4 $

I got stuck on this problem: Given a convex quadrilateral of area $S$ and sides $a$, $b$, $c$ and $d$, prove that: $$S \leq \frac{(a+b)(c+d)}4$$ What I've done so far was to proof that ...
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0answers
20 views

Proof of Menelaus using areas

I've tried to proof Menelaus' theorem using areas, but I've didn't figure out how. Some suggestions would be appreciated. Menelaus' Theorem states : Given a triangle ABC and a transversal ...
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2answers
51 views

Maximizing area under $y=e^{−{∣x∣}}$

The coordinates of the point $M(x,y)$ on $y=e^{−{∣x∣}}$ so that the area formed by the coordinates axes and the tangent at $M$ is greatest is what? I tried to plot the graph but after that I'm not ...
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1answer
25 views

Using Tan to find the area of a triangle

I have come across a question that I can't seem to figure out. If tanA = 3/4, find the area of the given triangle without using a calculator The given triangle is an scalene triangle with a ...
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1answer
57 views

Find the area of the shaded section on a square.

In the diagram,the curved paths are arcs of circles centered at vertices $A$ and $B$ of a square of side $6$. Find the area of the shaded section $BCD$. I've been stuck on this problem for days. I ...
2
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2answers
43 views

Quadrilateral's area problem

I have some troubles with this problem : Let $ABCD$ be a convex quadrilateral. $M$, $N$, $P$ and $Q$ are the midpoints of the sides $AB$, $BC$, $CD$ and $AD$. $AN$, $BP$, $MD$ and $CQ$ are ...
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2answers
44 views

Use calculus to find the area bounded by the circle $x^2+y^2-2x-2y-23=0$ and the pair of lines $x^2+2xy+y^2-7x-7y+12=0$

Use calculus to find the area bounded by the circle $x^2+y^2-2x-2y-23=0$ and the pair of lines $x^2+2xy+y^2-7x-7y+12=0$. I tried to solve the two equations by subtracting them. $2xy+35=5x+5y$,on ...
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0answers
24 views

Collinearity problem (Newton-Gauss line)

I had some troubles with this problem : Let $ABCD$ be a convex quadrilateral. $M$ and $N$ are the midpoints of the diagonals $AC$ and $BD$. The sides $AB$ and $CD$ are extended until they ...
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1answer
40 views

Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$

Someone asked me this question which I am really stuck at, any help is appreciated. If $a,b,c,d$ are the sides of a quadrilateral and $m,n$ are diagonals of the quadrilateral, then prove that ...
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5answers
426 views

What is the least number of (fixed) parameters I can ask for, when calculating area of a triangle of unknown type?

I need to calculate the area of a triangle, but I don't know, whether it is right angled, isoscele or equilateral. What parameters do I need to calculate the area of a triangle of unknown type?
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1answer
33 views

Area calculation

How could we best approach calculating the area inside $r=\cos^{2n-1}(x)+\sin(x)$, $0\leq x\leq \pi$, for $n=1,2,...$? For $n=3$ we get the following "potato/bean" graph: and for $n=51$ we get ...
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2answers
51 views

Find area of region that is common to both squares.

A 3-meter square and a 4-meter square overlap as shown in the diagram.D is the center of the 3-meter square. Find the area of the region DGFE. I 've tried to form right triangles in such region but ...
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1answer
14 views

Finding the area between three curves in which one is a piecewise function

Let $f(x)$ be a continuous function given by $$f(x)=\begin{cases} 2x,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |x|\leq1\\ x^2+ax+b, \ |x|>1\end{cases}$$ Find the area of the region in the third quadrant ...
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1answer
38 views

Fraction of circle contained in another circle passing through its center.

Consider a circle $C$ with radius $r$. Now take any point on the boundary of the circle, say $P$, and draw another circle $C'$ with $P$ as the centre and radius $k\cdot r (0\le k \le 2)$. Now what is ...
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2answers
50 views

area and perimeter of this figure [closed]

What are the area and perimeter of the union of the circles in the picture, where $r$ is the radius of both circles?
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1answer
34 views

Finding the area of an open rectangular tank

I tried approaching this as a normal rectangle, but my answer doesn't seem to be in the options. Here's the question - An open rectangular tank: 4m long, 3m wide and 4m high is made out of a thin ...
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1answer
24 views

Area enclosed by polar curves

Given $$r_1(\theta)=2(1+\cos\theta) \\ r_2(\theta)=2(1-\cos\theta)$$ I want to find the area of the region resulting from the intersection of those curves. Is the following integral correct? $$ 2A= ...
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65 views

Definition: vector or point belonging to an area

This is an applied problem, which I try to define mathematically. I have two vehicles, vehicle 1 is defined by the area, dependent on length $L$ and width $W$ of the vehicle, according to: ...
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1answer
42 views

How many total square feet is my driveway? [closed]

I need to know how many total square feet my concrete driveway is. I do not have an exact width or length, but the driveway is 23.5 square yards at 4 inches deep. How many total square feet of ...
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1answer
36 views

The line $y=k$ intersects the curve $y=2x-3x^3$ in the first quadrant

The line $y=k$ intersects the curve $y=2x-3x^3$ in the first quadrant as shown in the figure.What is the value of $k$ for which area of the shaded regions are equal? My try:I tried to find point of ...
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1answer
34 views

Finding fomulas for hyperbolic functions

I'm trying to find formulas for hyperbolic functions, starting with this image Knowing that the area between the origin, vertex and a point on hyperbola (enclosed by x-axis and hyperbola itself) is ...
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2answers
69 views

A simple area problem

I found this problem from a book (level = grade 7). In the attached figure, ABCD is a square with sides 10 units. Need to find the area of the quadrilateral PQRS built inside it as shown. The only ...
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0answers
25 views

How do you calculate an area enclosed by four tangents by using the integration method?

For example, make it $y=3x-6$, $y=3x-15.48$, $y=-0.25x+1.25$, and $y=-0.25x-1.06$. It's been taken by finding the tangent line of a curve $y=(x-2)(x-3)(x-5)$.
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4answers
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Area of a triangle with sides $\sqrt{x^2+y^2}$,$\sqrt{y^2+z^2}$,$\sqrt{z^2+x^2}$

Sides of a triangle ABC are $\sqrt{x^2+y^2}$,$\sqrt{y^2+z^2}$ and $\sqrt{z^2+x^2}$ where x,y,z are non-zero real numbers,then area of triangle ABC is (A)$\frac{1}{2}\sqrt{x^2y^2+y^2z^2+z^2x^2}$ ...
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1answer
15 views

Optimizing space for many shapes within an irregular shape

So let's say in a state, there are 50 schools dispersed throughout, given by Latitude Longitude points. How would we create distinct zones that optimize the space around each school? The goal is to ...
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1answer
89 views

Why prove that area is unique?

in the book Apostol's Calculus Volume 1, in the proof of the area of under of the parabola $x^2$ from $x=0$ to $x=b$ it is shown that the area $A$ must satisfy ...
3
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0answers
65 views

Is my proof rigorous? (Archimedes area of parabola)

I am currently reading Apostol's Calculus volume 1 and was revising the part where the area of a parabolic segment is found. I decided to write my own proof similar to the one in the book, which I ...
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0answers
975 views

How do I calculate the area the Wigner Seitz cells cover in a square?

It's my first time here, so I appologise in advance if I break any rules through this post. So I have a Cartesian Lattice spanning across the Euclidean plane and a unit square. The lattice points ...
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1answer
28 views

Any idea how to approach this problem

A rectangular meadow will have a fence around it. The long side is $130$ m longer than the short side. The sides lengths can be written $x$ and $x+ 130$. Write a simplified expression for 1) ...
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1answer
47 views

Clarify formula that computes number of dies on wafer

I want to compute the number of dies per wafer (also DPW in the following). There are some formulas, that can be used to do so: ...
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2answers
59 views

Area of regular n-gon without trig?

As the title suggests I'm trying to find a formula for the area of a regular n-gon that doesn't use trigonometry. I already know the trig formula and I realize that my question is simply asking for ...
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2answers
54 views

given 3 circles, find relation of the regions

I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard. I had no idea how to find it nor where to start Note ...
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3answers
231 views

Finding the area of a square that has a circle inside itself

I tried to solve the following problem: I think the image is self-descriptive. I tried to draw a vertical line from the top-end of $\theta$ angle to the horizontal line, then tried to use the ...
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votes
2answers
52 views

How to find the area under a semicircle using integration? [closed]

How would I go about finding the area under a semicircle? I know that to use integration the formula is $\int_a^b f(x) \mathrm{d}x.$However, when I put this into my graphing calculator it doesn't ...
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2answers
32 views

Find total area under infinite curves

My question is finding the total area covered by curves, such as the total area every curve in the following picture covers (from 100 on y axis to 200 on x axis): In my case, the curves are ...
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1answer
50 views

Triangular Area on hyperbolic surface

I have read numerous paper over area calculation in hyperbolic geometry but just can't seem to understand how to calculate a triangle's area in hyperbolic geometry. It would be nice to have a proof ...
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4answers
81 views

Find the area of the shaded region in the figure

Find the area of the shaded region in the figure What steps should I do? I tried following the steps listed here https://answers.yahoo.com/question/index?qid=20100305030526AAef8nZ But I got 150.7 ...
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7answers
604 views

Wanted : for more formulas to find the area of a triangle?

I know some formulas to find a triangle's area, like the ones below. Is there any reference containing most triangle area formulas? If you know more, please add them as an answer ...