For questions about area of plane figures.

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2answers
40 views

A silly question regarding square meters

Suppose we have two areas: $B$ of size $4m^2$ and $A$ of size $2m^2$. What is the ratio between their sizes? A simple division would yield 2, but I think that the answer is 4, as illustrated below: ...
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0answers
26 views

Area of the portion of the cylinder $x^2+y^2 = 9$ for which $-1 \leq z \leq 2$ and $ 0 \leq \theta \leq \pi/2$

Problem: Find the area of the portion of the cylinder $x^2+y^2 = 9$, for which $-1 \leq z \leq 2$ and $ 0 \leq \theta \leq \pi/2$ I first solved this by parametrizing the surface. $x = 3\cos(u)$ , ...
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2answers
28 views

Finding the Value of K in an Integral Function

Given the function $$f(x)\begin{cases} -2(x+1), & \text{x $\le0$} \\ k(1-x^2), & \text{x $\gt0$} \\ \end{cases}$$ Find the value of k for $$\int_{-1}^1f(x)dx=1$$ Wasn't really sure how to ...
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1answer
34 views

Finding the area of an equilateral triangle on an ellipse

The question is as follows: Let $E$ be an ellipse with major axis length $4$ and minor axis length $2$. Inscribed an equilateral triangle $ABC$ in $E$ such that $A$ lies on the minor axis and $BC$ is ...
2
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1answer
13 views

Smallest triangle in a convex polygon triangulation

I have been working on this problem for quite a while and it seems necessary to prove or disprove this particular problem. Suppose $T$ is the set of all possible triangles made from the vertices of a ...
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1answer
8 views

Left & Right Area Approximation Using Y-Axis - Method Alternatives

Is there a simpler way of solving this then calculating x1(h)+x2(h)+x3(h)+x4(h) by using the given y values (in this case h, the height is one, because the length of each rectangle is one) ...
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1answer
32 views

Finding the area of an irregular shape

This is probably a stupid question but if I have the number of sides of an irregular shape and the length of each side is there a way to find out the area the shape without knowing what the shape is? ...
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0answers
72 views

Why does base*height work?

I want to rigorously prove the idea that Base*Height=Area works (I do realise there are shapes which do not satisfy this equation). I think I can see why it works for integer values, but I want ...
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1answer
21 views

What is the value of $a$ so that this condition holds?

Let $f(x) \colon= x-x^2$, $g(x) \colon= ax$. Determine the value of $a$ so that the region above the graph of $g$ and below the graph of $f$ has area equal to $9/2$. Here $f(x) - g(x) = (1-a)x - x^2 ...
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2answers
56 views

How are these two integrals related?

How to express the integral $$\int_{-2}^{2} (x-3) \sqrt{4-x^2} \ dx $$ in terms of the integral $$ \int_{-1}^{1} \sqrt{1-x^2} \ dx?$$ I know that the latter integral is equal to $\pi / 2$. We can't ...
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2answers
27 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
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2answers
92 views

What is the area of a 12cm square? [on hold]

I am working through a maths revision sheet based on measurement and I have come across a question that simply states, what is the area of a 12cm square?
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2answers
40 views

What is the area bounded by these curves?

Let $f(x) \colon = x^2$, $g(x) \colon= x+1$. Then what is the area bounded by the graphs of $f$ and $g$ between the vertical lines $x= -1$ and $x= (1+\sqrt{5})/2$? My effort: Since $$ f(x) - g(x) ...
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0answers
30 views

A continuous centerpoint of a convex spherical polygon

In discrete geometry, a centerpoint $c$ of a discrete set $S$ of $n$ points in the plane is such that any half plane containing $c$ contains (roughly) $n/3$ points of $S$. (Such a centerpoint always ...
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1answer
67 views

Evaluate the area of the region bounded by the ellipse, where is my mistake?

$ (10x^2+6xy+y^2=2)$ => $ ((x/\sqrt2)^{2} + ((3x+y)/\sqrt2))^{2} = 1 $ so if I change the variables to $u$ and $v$, $u = x/\sqrt2$ $v= (3x+y)/\sqrt2) $ Then my bounds of integration become $-1 ...
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1answer
24 views

Ambiguous Limits in Area Determination

I am to find the centroid of the area bounded by the curve $y=8x^3-24x+11$, the $x$-axis and the line $x=-1$. Now I know that the centroid requires me to find the area under the curve first. I have ...
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2answers
36 views

Area of a segment

Two circles of radii 5cm and 12cm are drawn, partly overlapping as shown. Their centres are 13cm apart. Find the area common to the circles?
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1answer
35 views

How to calculate volume from surface area

I wanted to see is there a formula or method to calculate Volume of a 3D geometry, exactly Cube, from total surface area??? Plz help me in this Thanks a lot….
3
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2answers
58 views

How to find the area of the shaded region? [closed]

How do i find the area of the following shaded region? The figure consists of two circles, one of radius $2r$ and the other of radius $r$. The distance of the center of the circle of radius $r$ from ...
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1answer
26 views

How to compute the area of this set in the plane?

Let $f$ be a non-negative function which is defined, bounded, and integrable on a closed interval $[a,b]$, and let $$ S \colon= \{\ (x,y) \ | \ a \leq x \leq b, \ 0 \leq y < f(x) \ \}. $$ Then is ...
2
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1answer
43 views

Area of a triangle whose each side is less than 2 and greater than1.

What is the area of a triangle if each of its sides is greater than 1 and less than 2? My Try:Let a,b,c be the sides of triangle,then ...
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2answers
640 views

The area of circle

The question is to prove that area of a circle with radius $r$ is $\pi r^2$ using integral. I tried to write $$A=\int\limits_{-r}^{r}2\sqrt{r^2-x^2}\ dx$$ but I don't know what to do next.
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2answers
36 views

Derivation of the formula for the area of a regular polygon given the side length.

There are many formulas for finding the area of a regular polygon- but this is the one I am interested in: $$A=\frac{S^2n}{4\tan(\frac{\pi}{n})}$$ where $n$ is the number of sides, and $S$ is the ...
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1answer
37 views

Given a polygon of n-sides, why does the regular one (i.e. all sides equal) enclose the greatest area given a constant perimeter.

This doesn't require much more than the title. I just need an explanation, but an algebraic proof would be a bonus. We can demonstrate this for quadrilaterals, a square is best as shown by this ...
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4answers
32 views

Area of a Circle Inscribed in a Square

A circle is inscribed in a square. The diameter of the circle is 12.4 mm. Find the area of the region that is outside of the circle and inside the square. Round the answer to the nearest tenth.
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2answers
29 views

Area of a Shape

A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section? Express answer to ...
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1answer
93 views

Calculate the areas in a circle

Short: I want to calculate the areas drawn in this picture: The coordinates P00, P10, P01, P11 and Pdata are given Long: I am a programmer and want to calculate these areas, but unfortunately I am ...
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0answers
11 views

Best convex bounding polygon from a set of given lines

Given a polygon $P$ and a set of predefined lines, I am looking for the subset of lines that creates the best fitting convex polygon with respect to $P$. In other words the area of an ...
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1answer
29 views

A square pool is surrounded by a concrete deck

A square pool of area $144 \, \text{m}^2$ is surrounded by a concrete deck of area $25 \, \text{m}^2$. What is the perimeter of the outside of the deck?
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1answer
21 views

Area of an ellipse proportional to integral of cross-ellipse distances?

I am curious if the area of an ellipse can be shown to be proportional to the integral of all cross-ellipse distances. Before I define cross-ellipse distance, I will give a motivating example from a ...
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0answers
50 views

How to establish this result using induction?

A point $(x,y)$ in the plane is called a lattice point if both coordinates $x$ and $y$ are integers. Let $P$ be a polygon whose vertices are lattice points. Then the area of $P$ is $I + \frac{1}{2}B ...
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0answers
29 views

How to establish the formula for area of a triangle using the axioms of area?

We have the following definition: AXIOMATIC DEFINITION OF AREA We assume there exists a class of $M$ of measurable sets in the plane (i.e. subsets of the plane whose area can be defined) and a set ...
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1answer
22 views

Area of triangle on a sphere (not spherical triangle)

How do I find the area of a triangle on a sphere, and the triangle is not a spherical triangle, for example, the triangle is formed with two geodesics and a line of latitude. Is there a specific ...
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1answer
27 views

The surface area of a ring: $\pi[(r+dr)^2 - r^2]$ or $2\pi r\,dr$?

I know this may be really simple but here it is nonetheless. Let's say that I have a ring with a radius of $r$ and width of $dr$. I'm trying to find the surface $dS$ of the ring. Isn't it $dS = ...
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0answers
28 views

Dividing an infinite plane into regions

I am currently working on a computer program for computing layout of graph-based diagrams. Their content is placed in an "infinite" 2D plane with cartesian coordinates in the center of the diagram. ...
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1answer
66 views

I know the perimeter of the rectangle but not the area. How do I find the length and width? [on hold]

The perimeter of the rectangle is 986. I don't know the area and I need to find the length and width. The problem states that the length is 199 ft more than the width. That is all the information that ...
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1answer
35 views

Finding the area of a triangle in terms of the radius of the excircle

Prove that the area of a triangle $ABC$ is $$\frac12 (b + c - a)r$$ where $r$ radius of the excircle opposite to $A$ and the rest of the symbols have their usual meaning. I started off with the ...
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1answer
128 views

What is a circle's area if its radius is $\pi$?

The area of a circle equals $\pi r^2$. If a circle's radius is $\pi$, what is its area? I believe the answer is $\pi^3$, right?
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2answers
68 views

Can anyone calculate the area of the top shape in this diagram?

http://postimg.org/image/w5f5moq7z/ The top shape on the diagram is the sensor that I need to calculate the area for. I have tried using the 2 elipses at the side and combining them together to get a ...
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1answer
45 views

calculate the area of this shape

It's a rectangle with 2 half elipses joined on the left and right side. The rectangle itself is 3.55 X 2.54 The width of the whole shape (rectangle with 2 elipses) is 4.195. Take away the width of ...
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2answers
36 views

Calculus Area Cubic curve

Why area bounded between the "line $AB$" and the "cubic curve" and area bounded between the "line $BC$" and the "cubic curve" is $16$ times?
2
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2answers
94 views

Formula for a surface of revolution

The curve $y=\sqrt{x^2+1}, 0\leqslant{x}\leqslant{\sqrt{2}}$, which is part of the upper branch of the hyperbola $y^2-x^2=1$, is revolved about x-axis to generate a surface. Find the area of the ...
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1answer
21 views

Area of triangle in a different coordinate system.

This is for an android application but I think it is too mathematical to put on normal SO. I have a coordinate system where the origin is (0, 0), and the x and y axis go from -1 to 1. This coordinate ...
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2answers
48 views

Does anyone know of any open source software for drawing/calculating the area of intersection of different shapes?

I would like to be able to draw any number of different shapes and determine the area of their intersections. I'm looking for free, open source software. I thought about trying to code something up ...
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2answers
44 views

Maximize are of rectangle with semicircles on left and right [closed]

There is a rectangle with semicircles on the left and right sides. You know that the perimeter is 100. Maximize the area of the entire shape.
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2answers
31 views

Find the maximum area of a parallelogram given that you know the perimeter

The perimeter of the parallelogram ABCD is 14, therefore 14=2(AB+AD) so AB+AD=7. I know that the sizes of AB, BC, CD and AD are natural numbers. How can I find the maximum area of the parallelogram? ...
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1answer
32 views

Area of a Trapezium/Trapeziod

I have no idea have to draw a trapezium on internet,so I will try to explain as good as possible and hopefully someone get what I mean. So let assume there are (slanted as in the figure is not exactly ...
2
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1answer
20 views

Why is the integral of the arc length in polar form not similar to the length of the arc of a circular sector?

So I learned that the area enclosed by a polar function is computed by $$A = \int \frac{r(\theta)^2}{2}d\theta.$$ Which, I learned, comes somewhat from the formula for the area of a circular sector ...
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2answers
80 views

Circle areas on squared grid

There is a circle. On 9 equal squares. Every square has some value assigned to it. Every square gets weight, depending of what percentage of it is circle (area-wise). I need to find circle radius, ...
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1answer
40 views

Total distance travelled in velocity-time graph

I figured out by using trapezium rule. Any other method to find out the total distance travelled by the car ?