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Questions tagged [area]

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

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3answers
70 views

Length and width calculation from area [closed]

I have a question: If I have a square that is $50\ ft$ by $50\ ft$ it equals to $2500\ ft^2$. Simple enough. Now, if I divide $2500\ ft^2$ area in half, that equals to $1250\ ft^2$. How do I know ...
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2answers
35 views

Why are there only two answers for this co-ordinate geometry question? [closed]

A co-ordinate geometry question reads "Find value of $p$ such that area of triangle $A (p,2p), B(-1,6), C (3,1)$ is $10$ sq. units. Only 2 values come for $p$. Why does that happen? Shouldn't there be ...
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3answers
52 views

Area by a single measure [closed]

There is a triangle whose area can be calculated just by knowing/measuring one of its sides. If it is not an equilateral triangle, what it could be ?
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5answers
227 views

find the area of a kite with integration

A stunt kite has the shape in the diagram below: How can I find the area using calculus integration. Can anyone help me start this question, I am not looking for the full answer. I assume I only ...
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2answers
84 views

Calculate the described squared circle

I need to calculate the described squared circle... with only given the length of the side (a). I need to calculate the area of described squared circle. How exactly is it done with only a side given?...
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1answer
28 views

area limited by curves [closed]

help find the integrate for find area. $$R=\{(x,y)\in R^2: x^2+y^2\geq1, x^2+4y^2\leq 4, x-y\geq0, y\geq 0\}$$ I know what the area is, but I find it difficult to form the integral, can you help me ...
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2answers
35 views

Is it possible to cover all circle area with infinite lines starting from the center? [closed]

Is it possible to cover all area of a circle of radius r>0 with infinite lines starting from the center?
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1answer
180 views

How to find the projected area in the x-y plane of an ellipsoidal cap rotated by angle $\beta$?

Image of an ellipsoidal cap I am trying to compute a part of the projected area in the x-y plane (base area) of an ellipsoidal cap rotated in the x-y plane by an angle $\beta$. So I am taking a point ...
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1answer
189 views

Arithmetic mean - geometric mean [closed]

Use arithmetic mean -geometric mean inequality to prove that perimeter of a rectangle is minimum with a given area if it is a square
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2answers
72 views

How can I find the area bounded by given curves?

Find the area bounded by the curve and the axes whose parametric equations are $$ x=a\cos 2\theta, \quad y=b\sin 2\theta, $$ where $0\leqslant \theta\leqslant\pi$ and $0<a<b$, from $x=0$ to $...
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1answer
70 views

Area of a polygon? [closed]

Polygon What is the area of this polygon. (question 70) Anyone think they can show me how it's done? The image is in link form posted above.
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1answer
45 views

Find the area included between the curves $x^2 +y^2 =a^2$ and $\sqrt{|x|} +\sqrt{|y|} =\sqrt{a}$ ($a>0$) and find its area.

Find the area included between the curves $x^2 +y^2 =a^2$ and $\sqrt{|x|} +\sqrt{|y|} =\sqrt{a}$ ($a>0$) .
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1answer
89 views

Area of enclosed smooth curve is always irrational for rational dimensions [closed]

I have the intuition that smooth curves that are enclosed cannot be possible in real world , so it must be the case that either the dimensions(parameters) that define the curve ( like the radius of ...
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1answer
62 views

Number of solutions: set of inequalities [closed]

Is it possible to analytically calculate the size (i.e. the area) of the solution set for the following inequalities: $1<a<5$ and $1<b<5$ and $1<c<5$ and $1<d<5$ and $a\neq c.$ ...
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2answers
42 views

How to know which transformation to use?

I'm working on a question that asks to: Find the area in the first quadrant bounded by the curves; $\ xy = 1, xy=5, y=e^2x, y=e^5x $. I would very much appreciate help solving this question (...
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1answer
43 views

How to calculate area [closed]

I need to calculate the area of the surface side obtained by rotating around the $z$-axis the graph of the function $y=\frac{z^2}{2}$, where $z\in [0,1]$. How can I do?
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1answer
101 views

Where does this formula for area of a triangle come from? [closed]

I'm not good at entering formulas into text editors so I'm going to paste a few lines of code here: Given an arbitrary triangle formed by points 1, 2 and 3, where side-lengths a, b and e are as ...
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2answers
693 views

How do you find the area of the region bounded by the polar curves [closed]

How do you find the area of the region bounded by the polar curves $r=4\sin(2\theta)$ for $0\le\theta \le 2\pi$?
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1answer
260 views

Calculate the area made with the quarter arcs of circles without Integration [closed]

Is there any simple solution to find the area made with the quarter arcs of the circles BLUE AREA without using calculus(integrating!)?
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1answer
420 views

Ellipse Segment Area of tank

How do you arrive at the formula area = (AB/4)[arccos(1 - 2h/A) - (1 - 2h/A)sqrt(4h/A - 4h2/A2)] from this website http://www.had2know.com/academics/ellipse-segment-tank-volume-calculator.html? ...
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1answer
38 views

Filling a pool. [closed]

i have a pool of 2 meter radius, and 1.5 height. The pool is a perfect Cylinder. How many bottles of 1 liter i have to spill into the pool, so it will be completely full. The Volume of the Cylinder is ...
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1answer
722 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 ...
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2answers
70 views

what is the area of the region [ (x,y):0<x , y<1 , 3/4<x+y<3/2 ] do'nt use area of triangle & squares by conventional method? [duplicate]

I was confused with the answer provided on my other question since it doesn't fit the expected answer given in a multiple choice question: (A) 9/16 (B) 7/16 (C) 13/32 (D) 19/32 I would like to ...
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1answer
45 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.]
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1answer
634 views

Solving for least surface area of a cylinder with a given volume.

I am doing an online course. The volume is given and I must find the most efficient cylinder, the cylinder with the least surface area. An equation is given and its equivalent. I am not understanding ...
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1answer
33 views

How do I find the area under a wave/quadratic?

The roots A and B are (-1,0) and (2,0) respectively.
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2answers
44 views

Radius of circle included in a certain area.

Area $A$ is defined as the area of intersection between $x^2+x-2$ and $3x+1$. If a circle $x^2+y^2=r^2$ fits inside the area $A$, then what is the range $0 < r < \dots$? At first, since it ...
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1answer
61 views

How to find the radius of the circle after adding the area of segment?

I am making a game where a circle can hit a wall an interact with it to simulate a ball hitting a wall. When the circle is 1/4 the radius through the wall the area of the part in the wall will be ...
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1answer
110 views

Inequalities about area and perimeter

"A gardener is laying out a rectangular lawn. His specifications are that the area $(A)$ must be greater than $40$cm but the perimeter $(P)$ must be less than $40$cm. if the width of the lawn $(w)$ ...
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1answer
56 views

The Jacobian of $(x,y)\mapsto (x+y^2,y+x^2)$ under the substitution $u=x+y^2$ and $v=y+x^2$.

I am given the map $(x,y)\mapsto (x+y^2,y+x^2)$. I am unable to find the Jacobian by making the substitution $u=x+y^2$ and $v=y+x^2$. Any hints would be appreciated. (I am trying to find whether the ...
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1answer
23 views

How do you find the area of this trapezoid

How do you find the area of the trapezoid $KCDL$?
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2answers
25 views

Normal Bell Curves Displaced by One Standard Deviation

I was just researching some statistics and ran into this problem: a)If we have two normal bell curves, displaced by one standard deviation, how large is the area of overlap? b)What is the proportion ...
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1answer
153 views

How to find the projected area in the x-z plane of an ellipsoidal cap rotated by angle β in x-y plane?

I have ellipsoidal cap rotated in the x-y plane by an angle $\beta$; where the axis size in x coordinate is 'a', the axis size in y-coordinate is 'b' and axis size in z coordinate is 'c'. I am trying ...
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1answer
85 views

Polygons with convergent area [duplicate]

Suppose that there is an equilateral triangle of area 10, call this $A_0$, we then trisect each side of this triangle, then cut off the corners, giving the polygon $A_1$, what is the area of this ...
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1answer
57 views

Confusion of area under the curve

Consider a parabola $y=x^2/4$ and point F(0,1). Let $A_1(X_1,Y_1),......,A_n(X_n,Y_n)$ be $n$ points on that parabola such that each $X_k >0$ and angle $OFA_k=k\pi/2n$ (where $k=1,2,3,\ldots,...
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1answer
58 views

Does the area of a triangle change when it has a fixed rectangle inside it?

I am solving optimization problems for calculus. One of the problems has a ladder extending over a 10 ft fence, leaning on a house 4 ft from the fence, like so: | <-house | | ------| | ------| &...
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1answer
26 views

Faster reaction rate with increased surface area

If the largest dimension of a CaCO3 tablet that can be packaged economically is 10 mm (meaning a radius can be a maximum of 5 mm). What would be the best shape for the shape of the tablet? By best, I ...
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1answer
35 views

Why is the area of the function -1 in this case? [closed]

I understand that I need to get the area of the shape from 0 to 2 and subtract the area of the shape from 2 to 4 to get the area of 0 to 4, but how do I calculate the area of the second shape?
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1answer
54 views

Expected area of the smallest closed rectangle [closed]

Three points are chosen independently and uniformly inside the unit square in the plane. Find the expected area of the smallest closed rectangle that has sides parallel to the coordinate axes and that ...
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3answers
89 views

Find the area between the curves: $y=x+1, y=-3x+13,y=-\frac{1}{3}x-\frac{1}{3}$

Find the area between the curves: $$y=x+1$$ $$y=-3x+13$$ $$y=-\frac{1}{3}x-\frac{1}{3}$$ I see this when I graph it, and it's not easy for me to understand what variable I should integrate with. Any ...
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2answers
1k views

Find the area of the region bounded by the graphs of $y = 1$ and $y = \cos^2(x)$ from $x = 0$ to $x = π$

Find the area of the region bounded by the graphs of $y = 1$ and $y = \cos^2(x)$ from $x = 0$ to $x = π$. $a. 0.785$ $b. 3.142$ $c. 2.576$ $d. 1.571$ I graphed it but I'm not sure what to do ...
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1answer
277 views

how to find the area of a wrapped cylinder

Find the number of rolls required to wrap a $330$ ft long cylinder with an initial diameter of $1.75$ inches $5$ times. Each Roll is .$408$ inches thick, $24$ inches wide, and $20$ ft long. Each wrap ...
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1answer
29 views

vectors: help solving part d?

consider a parallelogram ABCD with A(3,-2,-1), B(2,1,3) and C(0,4,1). a-find the coordinates of D b-calculate the area of this parallelogram c-calculate the area of triangle ABD and that of ABC. d-...
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1answer
45 views

Find the area between the curves on the graph $y=\sin^2 kx \ $and $\ y=\cos^2 kx$

I think I would know how to approach this question if it weren't for the constant $k$ in the equations. I would usually find the point of intersection between the two functions and set the $x$ co-...
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1answer
112 views

Minimum placement of circles in polygon

I have a variably sized 4 sided polygon in 2D space. I can draw circles inside this polygon which have a fixed radius (500 meters). I need to cover all the surface area of this polygon, using these ...
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3answers
88 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
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1answer
44 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 ...
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1answer
309 views

Rate of área change according to its diameter

The area A of a circle is related to its diameter by the equation A=πD²/4. At which rate approximatelly the area vary in relation to its diameter when D = 10m?
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1answer
37 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
1k views

Surface area of $y = \sin(\pi x)$, from $x=0$ to $2$, rotated about the $x$-axis.

When I use the surface area formula I get 0, and Wolfram got zero as well when I use the bounds 0 to 2, why is this? However the solution manual uses the integral with bounds 0 to 1.. What is going on?...