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

learn more… | top users | synonyms

0
votes
3answers
39 views

Find area of shaded area in curve with range of values for $y$

The parabola in the diagram has equation $y = 32 - 2x^2$ The shaded area lies between the lines $y=14$ and $y=24$ Looking at the graph, I only need to find half the area and multiply by ...
2
votes
1answer
27 views

Prove surface area of a sphere using solid of revolution surface area formula.

I have to prove the surface area of a sphere with $r=1$ using the solids of revolution through revolution abouth both the $x$ and the $y$ axis. The formulas are easy. From top to bottom, surface area ...
1
vote
0answers
33 views

The area of trapezium is given by $A=(a^2-x^2)(x+a)$. Find x for the area to be a maximum and find A max.

For the diagram, the area of trapezium is given by $A=(a^2-x^2)(x+a)$. Find $x$ for the area to be a maximum and find $A$ max. Hi, I'm not sure how should i do this question. Can anyone help me with ...
22
votes
3answers
2k views

Where does the gap come from? [duplicate]

Can anyone tell me please where does the gap come from? Thanks and sorry if the question is not exactly relevant, I just didn't know where else to ask.
-1
votes
1answer
26 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 ...
0
votes
2answers
38 views

question about integration of symmetrical graph to find area

let's say, we have an symmetrical curve such as $x=\sqrt{y}$ If we integrate from 4 to 0, wouldn't it cancel out with the area on the other side of the axis? When integration is performed from 4 ...
0
votes
1answer
23 views

Double integral of off centre circle.

I have the vector field $F = (3xy,-x)$ along the circle $c$ (counter clockwise) which has a radius $a$ and centre $(a,0)$. I want to try and apply Green's Theorem to this, where I obtain $\int\int(-1 ...
0
votes
0answers
25 views

Geometrical interpretation of complex exponential integral

Coefficients of Fourier series of a function $f$ are computed by multiplying $f(x)$ by the exponential term $e^{-inx}$, then by integrating $f(x)e^{-inx}$ from $-\pi$ to $\pi$ and dividing by $2\pi$ ...
1
vote
1answer
48 views

Area bounded by$ y^2=x^2(1-x^2)$

Find the area bounded by $y^2=x^2(1-x^2)$? I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
2
votes
3answers
35 views

The Area of Trapezium is given by $A=\frac{1}{2}(4-x^2)(2x+4)$

The Area of Trapezium is given by: $$A=\frac{1}{2}(4-x^2)(2x+4)$$ Find the Maximum area of Trapezium. Hi, can anyone help me with this question. I know we differentiate the equation, but i don't ...
1
vote
2answers
64 views

If three cevians are concurrent at a point and form triangles of equal area, the point is the centroid

Let D,E,F be points on side BC,CA,AB of triangle ABC. The three cevians are concurrent at a point G. The areas of triangles BGD, CGE and AGF are equal. Prove that G is the centroid of ABC I ...
1
vote
1answer
40 views

Finding area inside circle and outside another circle

I was trying to find the area inside the circle $r=-2\cos(\theta)$ and outside $r=1$ and the upper bound was $2\pi/3$ while the lower bound is $0$. Is this correct? If not please help me set this up. ...
0
votes
0answers
21 views

Rectangle-Rectangle Intersection Area - Area Only

Suppose I have two rectangles that are not necessarily axis-aligned. What is a fast way to calculate their intersection area? Note that I am aware of convex polygon intersection and area algorithms; ...
1
vote
2answers
39 views

Explain finding the area of a region?

How is the area of the region inside the lemniscate $r^2 = 6\cos(2\theta)$ and outside the circle $r = \sqrt3$ equal to $(3(\sqrt3) - \pi)$? Thank you for anyone that helps.
2
votes
1answer
34 views

Area of the shaded region of a circle

The parallelogram ABCD has a larger altitude of 4 cm and a shorter altitude of 3 cm. What is the area of the shaded region? The figure doesn't show to which side each of the altitudes are related, ...
1
vote
0answers
27 views

How to calculate joint area of circles defined at each point on a continuous curve

Given a curve c (x(s),y(s)) in a 2D space (shown in red) and a radius function r(s) which gives the radius of a circle at that point. The red curve c(s) thus is the union of all centers of the ...
1
vote
1answer
22 views

Changing the side of a triangle without changing area?

$\triangle ABC$ has vertices $A=(8,2)$, $B=(0,6)$ and $C=(-3,2)$. Point $C$ can be moved along a certain line with points $A$ and $B$ remaining stationary so that the area of $ABC$ will not change? ...
10
votes
3answers
107 views

Closed form for the area of a convex cyclic n-gon, given the set of edge lengths

Let's say we are given a set of positive reals, and we're told that these are the edges of a convex cyclic $n$-gon, and we must compute it's area. For $n = 3$ there is the famous Heron's formula: ...
0
votes
4answers
24 views

Finding the area under the given parameters

Q: Find the area defined by $1 < |x-2|+|y+1| < 2$ After trying a lot, I asked my friend to solve this and she got the correct answer (which is 6) by shifting the origin to (2,-1) and then ...
0
votes
1answer
26 views

What are the coordinates for the center of the second circle? (Full question in body)

Full Question:A circle has its center at (6,7) and goes through the point (1,4). A second circle is tangent to the first circle at the point (1,4) and has one-fourth the area. What are the coordinates ...
2
votes
0answers
29 views

Area of a quadrilateral knowing the lengthes of its sides and diagonals

I have the length of four sides and two diagonals. Sides' lengthes are: AB 26ft; BC 36ft; DA 27.4; CD 35.8ft Diagonals' lengthes are ...
1
vote
1answer
32 views

Green's theorem area formula

I am assigned to calculate the area beneath the curve $y=x^2$ and above the $x$-axis using the formula $$A=\frac{1}{2}\int_C x\,dy\,-y\,dx$$ from $0\le x\le2$ while this seems simple to me I ...
2
votes
2answers
38 views

Is there a way of determinine the side lengths of a isosceles triangle knowing its angles and area?

I want to be able to determine the side lengths (or at least one side length) of an isosceles triangle knowing only its surface area and angles. Is this possible?
1
vote
1answer
39 views

Find the surface area of the portion S of cone within cylinder

Find the surface area of the portion S of the cone $z^2=x^2+y^2$, where z≥0, contained within the cylinder $y^2+z^2≤81$. The work I have is that I parameterized the cone into polar coordinates. ...
1
vote
2answers
29 views

How do I find the area between 3 curves?

I have three equations: $y=3/x$, $y=12x$, and $y=x/12$, $x>0$. I am not sure how to go about integrating an equation once I find the intersections. Do I need multiple integrals?
3
votes
2answers
40 views

$f(x)=x^a$ Definite Integral

Consider $f(x)=x^a $ Now $\int_0^1 x^a = 1/(1+a)$ gives the area bounded by the function, $x $ axis, $x=0$ and $x=1$. Now consider $a<-1$ On LHS the function is positive for all $0<x<1$ ...
0
votes
0answers
27 views

When do we need to separate areas while calculating definite integrals?

Many times when the function has range $f(x) \lt 0$ and also $f(x) > 0$ and we want to calculate an area of the function we need to separate the area in two parts. Thus, we will calculate the whole ...
0
votes
1answer
38 views

calculate the surface of the manifold in $\Bbb{R}^4$

How to calculate the surface area of the following manifold : $$ x_1^2 + x_2^2 = x_3^2 + x_4^2, 0 \le x_1^2+x_2^2 \le a^2$$ I know I should first describe this manifold as a map or a graph of a ...
3
votes
1answer
28 views

additive integral property

There's a common property of definite integrals: $\int_a^bf(x) \, dx=\int_a^cf(x)\,dx+\int_c^bf(x)\,dx$. I've often seen it said that $c$ must lie in the interval $[a,b]$. However, is this really the ...
0
votes
3answers
54 views

Prove that arc length for $f(x)=e^x/2+e^{-x}$ equals area under the curve

I've been tasked to provide a proof for the following: for $$ f(x)=\frac{e^x}{2}+e^{-x} $$ show that arc length of the curve over any interval equals the area under the curve for the same interval. ...
1
vote
2answers
19 views

Application of Integration Trig Function Area Problem

this is my question prompt. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. $y=4\cos(x)$ ...
0
votes
1answer
11 views

3D Surface Area Integral

find SA of the cone $$z=2\sqrt{(x^2+y^2)}$$ bounded by $$y=x$$ and $$y=x^2$$ in the first quadrant. This is my integral setup for the surface area of that portion of the cone, what did I do wrong? ...
8
votes
7answers
207 views

Area of a circle $\pi r^2$

So, today I learned that the area of a circle is $\pi r^2$. So, I thought that since $r$ is $1$ dimensional, $r^2$ will be $2$ dimensional. In this case, a square, as you only multiply $2$ dimensions ...
3
votes
2answers
54 views

1987 AIME Problem #4

The Question: Find the area of the region enclosed by the graph of $|x-60|+|y|=|\frac x4|$. Answer: What I know: Because of all the absolute values I only need to find one side of the graph of ...
1
vote
2answers
55 views

Eccentric circles

I have an equation to calculate the distance to the outside of a circle from an eccentric point within the circle. $$x = E\cos(a) + 0.5\sqrt{(D^2) - 4*(E^2)\sin(a)^2}$$ Where: $E$ = eccentricity, ...
0
votes
1answer
18 views

Ratio of areas in triangles with Cevians

Can someone show me how to solve this problem as they normally would? It would also be very helpful if you could also give me a mass points solution. I know mass points works for ratios of segments, ...
0
votes
0answers
22 views

The Area of Something Known Only in Volume

In my worldbuilding, I have created a plain of lava that extended to a volume of 59 to 77 million cubic kilometers and 4500 meters at the thickest. As I understand it, the basic formula of volume is ...
0
votes
1answer
24 views

Can't find the area of a polar region

I've ran into a bit of a stopper on this one problem. I solved this other problem like this yesterday but this one seems to cancel itself out to zero. I'm not sure what I'm doing wrong with this ...
0
votes
1answer
30 views

surface curved shape

Complete noob in Math here. I have a surface that I need to calculate the surface area from This shape (the surface IN the red line) I understand that I can divide the 'room' in different shapes to ...
1
vote
1answer
36 views

Help with a double integral

I'm not calculating the following integral correctly, but can't for the life of me find what I've done wrong. Here's my work: $$ \int_0^{13} \int_0^{\sqrt{169-x^2} } dy\ dx $$ $$ \int_0^{13} ...
2
votes
1answer
27 views

General Triangles: Area, lengths and angles calculations

I have a question on General Triangles (as in non right angle). I’m trying to create a program that calculates angles and sides based on the user entering Area and some sides length or angle ...
0
votes
2answers
37 views

The most efficient way to calculate the area of the triangle

What is the most efficient way to calculate the area of the triangle enclosed in the lines with equation $y= x+2, 2y= -3x + 7$ and $x=5$? I constructed all the lines and then calculated the sides of ...
1
vote
2answers
51 views

Area of region bounded by two parabolas using double integrals

The questions asks: "Let R be the region in the first quadrant bounded by the graphs of the parabolas $y=2x^2$, $y=9-x^2$ and the line x=0. Express the area of region R: (i) Integrating first with ...
0
votes
1answer
68 views

How to calculate the surface area of a normal chicken egg by using calculus? [duplicate]

I am recently doing my IB Maths HL internal assessment and my topic is how to calculate the surface area of an egg. I want to apply calculus knowledge into this question but my knowledge about this ...
0
votes
0answers
59 views

What is the cap body produced by the unit sphere?

For ecach number a > 1, let C(a) be the cap body produced by the unit sphere in E^(3) and the points (+-a,0,0). Calculate the volume, surface area and mean width of C(a). For this question, I don't ...
0
votes
1answer
40 views

How is the disk method used to calculate surface area of an egg? Is it possible? [closed]

I am trying to calculate the surface area of an egg with the disk method, but $\int ab2\pi f(x)\,dx$ does not come up with the right answer. I understand how the formula works to calculate volume, but ...
0
votes
0answers
22 views

how can I calculate covered area under a single-slope roof?

I'm looking to build a small covered patio area on our property, next to our pool. It'll be open on all sides, and covered by a simple skillion/single-sloped roof. So something like in this photo: ...
4
votes
1answer
79 views

Area covered by Moving Circle?

Consider a situation where we have a point (x,y) moving on a 2-D plane. In fact, the point is function of time x=f(t),y=g(t). Centered around (x,y) is a circle of radius r? Obviously, we can visualize ...
0
votes
3answers
41 views

Find area of triangle ABC given areas of sub-triangles

The line p is parallel to the the side AB of triangle ABC and splits the sides AC and BC in points D and E, respectively. If the area of triangle ABD is m and the area of triangle AEC is n, find the ...
3
votes
1answer
37 views

Show that the equation of the normal line with the minimum y-coordinate is $ y = \frac{-\sqrt{2}}{2}x + {1\over k}$

Question: The curve in the figure is the parabola $y=kx^2$ where $k>0$. Several normal lines to this parabola are also shown. Consider the points in the first quadrant from which ...