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.
3695 questions
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How to calculate the area of a parabolic dish

I feel like this should be really easy, but I'm not sure if I'm doing it correctly so I'm going to give it a go here, and if I'm not very good at maths (I'm not) then you can hopefully correct me! Suppose I want to paint the surface of a parabolic…
Jamie Twells
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Surface Area of a Sphere Without Calculus

I'm having trouble with finding the surface area of a sphere, without using any calculus. What I thought, was that the surface area of a sphere is fundamentally an infinite number of rings, decreasing in size as you go up or down the actual…
StopReadingThisUsername
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Finding the area of shaded region with overlapping identical triangles

Triangles $ABC$ and $DEF$ are identical with $EF=10, EO=2, CO=6.$ Find the shaded area. I have tried my best to solve the area-finding question mentioned below, but nothing is working out. So anyone interested in helping me out with this…
Mona
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Unit of area based on the radian

I was looking at the answers to Why square units? and I felt that the discussion was bogged down by all the talk about circles instead of showing what's special about the unit square area, so I'd like to ask a follow-up question: Suppose we took the…
Francis Ocoma
  • 529
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Find height of irregular trapezoid with known angles and surface area

KNOWN: Length DC Alpha Beta Surface S NEEDED: Height h For an algorithm, I require a way to solve this for any trapezoid. Sort of like this question (Given a known isosceles Trapezoid find height of another with same angles & one base but…
DragonGamer
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Formula to calculate surface area of an irregular shape

I have to put some data together for a presentation on lakes that will be affected by a rule change. I have a table with the surface area of the lake and the length of shoreline. I need to calculate the inner surface area of the lake if I move in…
Alith7
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Converting area of a rectangle

This is probably a very simple question and I'm being stupid. Let's suppose I have a rectangle that is 0.6m by 0.4m. To calculate the area of this rectangle, you do 0.6 multiplied by 0.4, which is 0.24m^2. However, if I convert the units to cm…
user798841
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Find area of shaded region between circles inscribed inside a square

Find the area of the shaded region such that the measure of a side of the square is $x$ unit. Here is my plan and incomplete solution: Step 1: I need to subtract the area of the circle from the area square and divide it by $4$. I denote the…
AYA
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enclosed area nearest to integer is

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=2\hat{i}+2\hat{j}+\hat{k},\vec{c}=5\hat{i}+\hat{j}-\hat{k}$ be three vectors. Then the area of the regin formed by the position vector $\vec{r}$ satisfy the equation $\hat{r}\cdot \vec{a}=5$ and…
jacky
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Is there any difference in definition of Area in maths and physics?

I am a little bit confused after reading the definition of area : The area of a shape can be measured by comparing the shape to squares of a fixed size.[2] In the International System of Units (SI), the standard unit of area is the square metre…
gpuguy
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Find the area bounded by $x= at^{2}$ and $y = 2at$ from $t=1$ to $t=2$

Find the area bounded by $x= at^{2}$ and $y = 2at$ from $t=1$ to $t=2$ I tried to solve this by integrating $\int_{1}^2 y \frac{dx}{dt} dt$ $\int_{1}^2 (4a^{2}t^{2}) dt$ $= (28/3)a^{2}$ What is wrong with my attempt$?$ Answer is given…
Mathaddict
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What will be area of $|x|+|y|\leq 1$?.

It is required to obtain the area of $|x|+|y|\leq 1$. Since, the required region will just be a square with the side one. So area should be $1$. Am I right? Thanks. The answer is in the range $1.90$ to $2.10$.
userNoOne
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Finding the area of a region of circle

Consider the following shape. It is requested to find the area of the shaded region. The radius of the circles and the overlapping half circles is 1 unit. The region is irregular and I couldn't find a way to find it.
Ahmad
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Fraction of Perimeter

If the side of a hexagon is increased from 20 cm to 24 cm, What fraction does the perimeter increase by? So,is it one side of hexagon is increased or all sides of hexagon is increased by 4 cm. I calculated by increasing all sides of the hexagon by 4…
geetha
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Calculate the surface area of this shape.

I am stuck at calculating the surface area for this shape (only red area). I know how to calculate some area, but not sure how to substract area $$P = \frac{20 \cdot 10}2 = 100 - 25\pi\, -\, ?$$
safety
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