Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [area]

Area is a quantity that expresses the measurement of the extent of a two-dimensional shape.

Frequent problems related to area include

  • Computing area of planar figures like triangles, circles, quadrilaterals, etc.
  • Computing the surface area of a figure in three dimensional space like a sphere or a cube.
  • Applying techniques of integral calculus to calculate the area bounded underneath the graph of a function, or the area bounded between the graphs of two functions.
  • Broadly discussing alternative definitions and notions of area.
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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 the nearest square foot.
IHeartBunnies
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folding two or more sheets of paper into one

I was wondering, whether or not it is possible to fold two or more DIN A4 sheets of paper into one sheet of paper, those are would be larger than the area of one single DIN A4 sheet of paper (and the resulting new sheet's area should be as large as…
Christopher Schmidt
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How to find the area of a Isosceles trapezoid given its diameter?

I have the diameter of an Isosceles trapezoid, and nothing else except the height. Is there any formula for finding the area of this shape with the given details? I've searched all over on Google, but couldn't find anything.
Abolfazl Malekpour
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Whats the projected area of a shape seen at an angle

If I have a 2D shape on a plane embedded in 3D cartesian space and I know the area of that shape. I would like to calculate the area of the projection of that shape when viewed with an orthogonal camera at a certain angle (angle 0 meaning viewing…
matthias_buehlmann
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Find the volume of a sphere whose area is 180 square meters. *

How would you begin to solve this? Do you use $A = 4\pi r^2$? $V = \frac43\pi r^3$. Substitute $180$ for $A$, solve for $r$ and plug into Volume equation(leave in simplified form).
Harry Iguana
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Question about approximating an area based on a graph

Here is the question and image: Hi, here is my attempt: Each block has an area of $(1/2)^2 = 1/4$ miles$^2$. This grey region covers $14$ blocks. So $14*1/4 = 3.5$. So the approximate area is $3.5$. However, the answer is $2.75$ miles. I do not…
Deadpool 36701
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Area and volumes of solids formed by revolution of curve

For finding the volume of a solid ( eg. Sphere ) we devide it into various strips which somehow look like a frustum of cone. And we find the area of this infinitesimal frustum area assuming upper and lower radius are almost equal and slant height…
ronak jain
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Area formed by lines passing through (4,6) with co-ordinate axes

Straight lines are formed passing through (4, 6) and forming triangles of given area with the coordinate axes (each line forms a triangle of fixed area with the axes).P,Q,R&S needs to be compared with the choice 1,2,3&4. (P) Number of lines…
Samar Imam Zaidi
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Find the dimension if the dining room is 4 square feet longer than its width, 96 square feet is given as the area

A dining room has a total area of 96 square feet. The dining room is 4 square feet longer than its width. What is the dimension of the dining room? The answer in the answer sheet shows this equation : 96 = 4x(x) In the end, the x equals to 4.9…
Mers Tho
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Area of the curve $y=\sin\theta \cos^2\theta$; $x=\sin^2\theta \cos\theta$ bounded by tangent parallel to axes

Area bounded by tangents of the curve given by $y=\sin\theta \cos^2\theta$; $x=\sin^2\theta \cos\theta$, which are parallel to co-ordinate axes(other than axes) is (1)$\frac{4}{27}$ (2) $\frac{27}{4}$ (3)$\frac{16}{27}$ (4) $\frac{27}{16}$ My…
Samar Imam Zaidi
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area of a helix

is anyone knows how to calculate the area of a ring that is twisted, for example an edge of a tooth of a thread coil, please see a picture (area between A and B points)
user3336272
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Area of Portion of Sphere from a inside Cube

The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style however, both the red and blue areas were a bunch of highly irregular…
Srestha
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find the area enclosed by $ f(x)=x+\sin(x)$ and its inverse from $x=0$ to $x=2$

I don't have a single clue to start, and we cant find the inverse so we must use some properties, but which ones? thanks
gajimono321
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Differential area for the lateral surface of frustum of a cone

I am studying Fluid Mechanics and I needed a differential area element of the side or lateral surface of a frustum. This frustum is cut from a cone. In solution manual of the book I study, differential area is given for side surfaces by $$ dA=2\pi r…
Ali Kıral
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Help indentifying unknown method of computing area by rolling a ball about the perimeter

Some time ago I saw a brief presentation about a newly discovered method used to compute the area of certain two-dimensional shapes by rolling a circle (of varying radius) about the perimeter; the area traced out by the circle was the area enclosed…
Galendo
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