For questions about area of plane figures.

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3
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0answers
38 views

Area of an equilateral triangle

Prove that if triangle $\triangle RST$ is equilateral, then the area of $\triangle RST$ is $\sqrt{\frac34}$ times the square of the length of a side. My thoughts: Let $s$ be the length of $RT$. ...
2
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1answer
38 views

Use determinants to calculate the area bounded by 3 vectors

I have seen the proof of why the area of the parallelogram created by 2 vectors $u = \left(\begin{matrix} u_1\\ u_2 \end{matrix}\right)$ and $v = \left(\begin{matrix}v_1 \\ v_2 \end{matrix}\right)$ ...
0
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0answers
32 views

Is Randall's model for a sling correct? [on hold]

In What If 116 Randall Munroe talks about ways to get drivers around a race track The 13th paragraph he imagines the drivers at the end of what seems like a big tether ball: Imagine a "vehicle" ...
2
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1answer
33 views

Area under the curve described by θ=ar

I'm interested in finding the area under the curve described by θ=ar, which is a linear curve with slope 'a' in polar coordinates. Here is what the curve looks like: ...
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0answers
30 views

What radius circle to remove from unit circle to make golden earring?

A circular lamina of radius $x$ is removed from a circular lamina of radius $1$. If the center of gravity is at the edge of the smaller circle (along the line connecting the two centers) what is $x$? ...
0
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1answer
26 views

Integration: Finding area, volume and arc length

I am new to integration, so please do not mark this question as "not enough research done" Here is the question (please open image in new tab to see it clearly) - I am getting stuck with the ...
0
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1answer
39 views

Area of triangle, variable sides. High school level. [on hold]

The triangle $PQM$ is inside the triangle $AOB$. a) Show that the area of the triangle $PQM$ can be expressed using the function $T$ given by $T(x) = -\frac{1}{2}x^2 + 3x \quad (0\leq x \leq ...
0
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0answers
21 views

Find the sub-area of a circle cut by chords [closed]

Suppose a circle of area $A$ is given, and then cut off portions using chords of the circle. What is the resulting area based on such chords?
2
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0answers
27 views

Perimeters Areas and Volumes

I have to write an article for a school magazine. I thought it is better to choose a simple topic like Perimeter, Area and Volume. I am looking for historical fact and surprising facts about ...
0
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0answers
32 views

Formula for area of circle made up of squares

I need to draw an approximate circle on a grid of squares and find its area. Each square must either be completely part of the circle or not at all occupied. Obviously, this means that it cannot be a ...
0
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4answers
77 views

Area of the curve sin(cos(x)) [closed]

Find the area of the region enclosed by the curves $y = \sin (\cos(x))$, $y = 0$ ,$x = π / 2$, and $x = −π / 2$. I am not able to integrate the function. How do I find this area?
1
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1answer
21 views

Integration about x and y axes to find area

I have a problem statement that requires me to find area between the curves about x axis and about y axis. But my answers are not matching. Please find below my worked out solution - The ...
-1
votes
2answers
614 views

Find the area of this irregular octagon inscribed in a circle [closed]

Find the area of the octagon pictured here I do have some ideas how to solve it, but do not want to write them down here, because I'm hoping to find some different approaches. Also, see 1978 ...
1
vote
1answer
26 views

Need Assistance with Calculating the Area of a Square when given the diagonal.

It's been several years since I've done this stuff---I'm trying to brush up for a Praxis exam in a few weeks. I've come across a problem I'm having a lot of trouble with. I'm given a square. The ...
-2
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1answer
30 views

Calculate the area between functions

[I need to find the area between this three functions, therefore I need to use Integral g(x)-f(x) but I tried and it gives me negative and enormous numbers.]
0
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2answers
37 views

Calculating if a point is within the overlap of two circles

Two circles of equal radius (R) intersect as shown below. Assuming more points are uniformly distributed in an area with dimensions D*D, where D = 4*R. What is the probability that a point will be ...
0
votes
1answer
26 views

Finding $y=b$ that dissects the area between $ y=36, y=12, y=x^2$ into 2 equal halves.

Finding $y=b$ that dissects the area between $ y=36, y=12, y=x^2$ . what I did is solving the following equation: $\int_{0}^{6} 36-x^2\,dx$ - $\int_{0}^{\sqrt{b}} b-x^2\,dx$ = $\int_{0}^{\sqrt{b}} ...
0
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0answers
8 views

Find the Area of 3d object? [duplicate]

I know I've asked a similar question, but I cannot get the answer. If some 3d object are $(1.2*10^4)$ times bigger than other 3d objects. What is the area of the 3d objects, in square meters, if the ...
-3
votes
1answer
33 views

Find the area of the spaceships. [on hold]

Some spaceships are $2$ x $10^4$ times larger than other spaceships used in other movies. Find the area of the spaceships in $m^2$ if the other spaceships had a surface area of $1378cm^2$. I don't ...
1
vote
0answers
27 views

Area of circles on a wall

If you are painting a wall that is 10 ft by 12ft blue with gray polka dots on it, and the polka dots are spaced their diameter's distance away from each other at the shortest distance, how much paint ...
0
votes
1answer
23 views

How to find percentage of one rectangles area based on another rectangles area

I know I might sound the dumbest person in the galaxy, but I just wanted to make sure I am doing this right. I have a rectangle say [R1] placed inside a bigger rectangle [R2]. R1 will always be <= ...
1
vote
3answers
57 views

How to determine $f(x)$ and $g(x) $for area between curves?

So if I'm trying to figure out the area between two curves, I understand that the formula is: $$\int f(x)-g(x) \mathsf dx.$$ But without them telling me which is $f(x)$ and $g(x)$, how do I tell ...
5
votes
3answers
215 views

Finding the area of the 4th triangle, given the areas of the other 3, and all the 4 form a rectangle

In one of my tutorial classes, when I was studdying in 9th class (I am in 10th now), our tutor gave us a problem saying it’s a difficult one, and to him, it was incomplete. This is that problem: ...
0
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1answer
19 views

Can ratios similar to those related to the surface area of a circle and sphere be applied to determine properties of a 3-sphere?

Applying the strategy of describing the surface area of a circle as a product of the ratio for the surface area of a triangle, reveals a consistency that also applies to the surface area of a cone. ...
2
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2answers
40 views

(surface) Area of an ellipse by integrating

Given is an ellipse with $x=a\cos(t),~~y=b\sin(t)$ I do this by using $S=|\int_c^d x(t)y'(t) dt|$, so calculating the area regarding the vertical axis. Since $t$ runs from $0$ to $2\pi$ I figured I ...
4
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1answer
166 views

Understanding probability

I'm stariting to study probability and some really interesting questions starting to bother me. Let's consider the unit circle $C$ and $D$ - the circle with radius $\frac{1}{2}$. I know that the ...
2
votes
2answers
51 views

Find the area of trapezium

$ABCD$ is a trapezium in which $AB||CD$. If $P$ is the point of intersection of diagonals $AC$ and $BD$ such that area of triangle $DPC=50cm^2$ and area of triangle $APB=32cm^2$.Then find area of ...
0
votes
2answers
59 views

calculate area of four leaved rose with $ r=cos(4\theta)$

This problem is from a past paper that I am doing, and I have managed to arrive to answer. However, it is different to what the examiners presented in their corrections. My approach to this problem ...
0
votes
2answers
33 views

Evaluate the integral over the region R

I am a bit lost on how to evaluate double integrals over a region. I am asked to evaluate the following integral $$\iint\frac{y}{(x^2+y^2} dA$$ over the region R: triangle bounded by $y=x, y=2x, ...
0
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1answer
27 views

drawing the polygon

I want to draw the polygon, its sides and area is provided. e.g. number of sides : 4 length of 1st side : 1 length of 2nd side : 2 length of 3rd side : 3 length of 4th side : 4 ...
0
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2answers
23 views

Finding an enclosed area using integrals

Find the area enclosed by $y=\frac 8{x^2}$, $y=x$, $x=8$ The answer says the area is equal to $27$. I tried dividing the area into $2$ (one of them a right angled triangle). I found the area of the ...
5
votes
4answers
138 views

How to calculate the area covered by any spherical rectangle?

Is there any analytic or generalized formula to calculate area covered by any rectangle having length $l$ & width $b$ each as a great circle arc on a sphere with a radius $R$? Note: Spherical ...
0
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3answers
49 views

Find unknown vertex of triangle given area and other 2 vertices

I need to find the coordinates of the 3rd vertex of a triangle given that I know the other 2 vertices and the area. The triangle is not guaranteed to be of any particular type (right, isosceles, ...
0
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2answers
31 views

Find the area between $x + \sin x$ and its inverse

I am confused this problem is really hard for me . I don't know how to calculate this function's inverse but my teacher said that this can be done without finding out the inverse of the function . ...
0
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1answer
28 views

Symmetry of the square of the reciprocal function

I always thought that $y=\frac{1}{x^2}$ was symmetric across the line $y=x$. However, when I computed the area between the function and the $x$-axis from $x=1$ to infinity, I got 1 $\int_1^\infty ...
0
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0answers
47 views

Calculating the area under the graph of a function.

I know this question might be very trivial for many of you, but I would appreciate if you take a look, in the following question I'm asked to calculate the area that is under the function's graph in ...
2
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3answers
59 views

Different ways to prove that area of circle with radius $r$ is $A=r^2\pi$

I want to compute the area of a circle in different ways. I know that any circle with radius $r$ have area $A=2\int_{-r}^r\sqrt{r^2-x^2}dx=r^2\pi$, but I want to prove it in other ways. My first way ...
0
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1answer
278 views

How do you find the cross sectional area of a Tetrahedron?

How is vector's related to this question? If so, how can you use the vectors? I understand that its a triangular pyramid. But how can you show the cross sectional area for any generalised height? ...
4
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1answer
80 views

Area of a square inscribed in a circle

ABCD is a square inscribed in a circle whose diameter is L cm. If P and Q are mid points of BC and CD, respectively, find the shaded area MDCNT Thanks I tried this If I knew the M value I could ...
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0answers
20 views

Number of grid points in a polygon

Following problem: I want to approximate the number of grid points in a polygon, based on the condition that the distance of the grid points are variable. What i need is an approximation, i am aware ...
0
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1answer
27 views

Finding $y$ In Calculus(Area) Problem? [duplicate]

Find the number b such that the line $y=b$ divides the region bounded by the curves $y = x^2$ and $y = 4$ into two regions with equal area.
0
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1answer
35 views

Linear Algebra: Compute Area of Parallelogram

I have this one Linear Algebra question that is asking me to compute the area of a parallelogram defined by 4 vectors. Here is the question: Let $\vec{u}=\begin{bmatrix}a\\b\end{bmatrix}$ and ...
0
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0answers
41 views

How to find the area between a quadratic function $f(x)=ax^2+b$ and a line $g(x)=c$?

How to find the area between a quadratic function $f(x)=ax^2+b$ and a line $g(x)=c$? So imagine you have the simple function $f(x)=x^2$ and the constant function $g(x)=2$ How can I find the area ...
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2answers
29 views

The $ABCD$ paralelograms sides are $AB,BC,CD,DA$. On these line segments there are points in the same order: $X,Y,Z,V$.

The $ABCD$ paralelograms sides are $AB,BC,CD,DA$. On these line segments there are points in the same order: $X,Y,Z,V$. We know, that: $$\frac{AX}{XB}=\frac{BY}{YC}=\frac{CZ}{ZD}=\frac{DV}{VA}=k$$ ...
0
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2answers
56 views

Why doesnt the gcse syllabus allow us to use herons formula?

I saw the answer to this question, it wants us to find the angle A using the cosine rule and then use the formula 1/2 ab Sin A to find the area. Why can't we just use herons formula - Area = (P ...
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vote
3answers
42 views

How to prove $2^{n+1} * 2^{n+1} = (2^n*2^n)+(2^n*2^n)+(2^n*2^n)+(2^n*2^n)$

Below diagram is used as part of a proof of induction to prove that $E$ a way to tile a $2^n * 2^n$ region with square missing : What is the proof that $2^{n+1} * 2^{n+1}$ = ...
2
votes
1answer
29 views

Spherical Triangle

I know that the area for a spherical triangle is calculated as Area $= r^2(a+b+c-\pi)=r^2E$ where $E= (a+b+c-\pi)$ is the spherical excess I was wondering why do you have to multiply by $r^2$ (the ...
0
votes
1answer
23 views

Find longer side of a rectangle with respect to another rectangle

So I have two rectangles: Rectangle R1 with width r1w and height r1h Rectangle R2 with width r2w and height r2h I can find the slope/aspect ratio of the two ...
0
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0answers
42 views

maximize partitioned area puzzle…

I took the time to draw this out. It's pretty simple and also very chicken scratch. I apologize for the crudeness and chicken scratch. The part of this that throws me off is the partitioned part. ...
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5answers
75 views

How do I find the area of this shaded circle?

This circle has been bugging me for a while, and I do not know how to solve it. Can someone help me find the area of the shaded circle? It would really help me.