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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The surface area of a sphere is..m

The surface area of a sphere is $102\ \mathrm{cm}^{2}$. If the sphere is cut into two hemispheres, what will be the change in surface area ?. My attempt; $$ \mbox{Surface area of sphere}\ = 102\,,\quad4\pi r^2=102\,,\quad r=2.8484\ \mathrm{cm} $$ If…
pi-π
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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? Any ideas will be most helpful thanks.
Rob Wilkinson
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Area of triangle AQB

How do we find the ratio of area of triangle AQB to area of square in this question?
oshhh
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Finding different surface areas along a frustum pyramid

New to the site so excuse any clumsy writing: I am attempting to write an equation that finds the surface area along a pyramid as you move up and down the height of it. I know the initial areas of the top and bottom and thought I could use the…
EngineeringSam
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Find area of region that is common to both squares.

A 3-meter square and a 4-meter square overlap as shown in the diagram.D is the center of the 3-meter square. Find the area of the region DGFE. I 've tried to form right triangles in such region but the only lenght i know is the altitude dropped from…
Nameless
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Area of irregular hexagon with all angles = 120 degrees

I want to derive a formula to calculate the area of a irregular hexagon which is guaranteed to have all internal angles = 120 degrees. Please guide me how to proceed to form a general formula.
Bhoot
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Find the area of the region in $X$-$Y$ plane: $\{(x,y) \in \mathbb{R}^2| x^2+y^2 \leq 144; \quad \sin(2x+3y) \leq0 \}$

$x^2+y^2=12^2$ is a circle having centre at $(0,0)$ & radius $12$. So,I could easily mark the first inequality. But $\sin(2x+3y)=0$ implies $2x+3y=n(\pi)$ where $n$ is any integer For $n=0$, $2x+3y=0$ & the graph is a straight line passing through…
Number
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formula for surface area without dimensions

If the radius of a cylinder is twice its height, write a formula for the surface area in terms of its height only. My textbook says the answer is $12\pi h^2,$ but I got a completely different answer if someone could work me through this it would be…
samantha
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Computing areas of equivalent size?

I have a small problem where I am stuck: I have values which describe a distribution. In particular I have the lower percentiles from $25.5\% - 50\% = 30 - 55$ and the upper percentile $50\% - 97.5\% = 55 - 83$. I would like to construct two…
Christian Sauer
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Help with writing an Equation for area?

You have 240 feet of wooden fencing to form two adjacent rectangular corrals. You want each corral to have an area of 1000 square feet. So far I have a drawing of a large rectangle, split by a line directly down the middle. This makes the 2…
Samuel
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Find an equation for the surface area of stacks of cubes that increase in size

The question asks one to find an equation to describe the change in surface area of stacks of 1 in by 1 in cubes. The first figure is a single cube, the second figure has a base of two cubes with one cube stacked on the left cube, the second has a…
Thalia
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Finding the actual area represented on a map

This question is similar to finding the actual distance represented on a map. The question is: Find the actual area, in m², represented by 1cm² on the map. The scale of map is 1: 180,000
lase
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Calculate Area (theoretically)

I have a garage with the surface X. These multiple vehicles with the surface Y. The vehicles shall have a distance Z from other vehicles or walls. How can I calculate that? I've started with an if who checks an Array how much vehicles are in that…
Webice
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Finding the area of an irregular shape

This is probably a stupid question but if I have the number of sides of an irregular shape and the length of each side is there a way to find out the area the shape without knowing what the shape is? i.e. I cannot use the method of breaking the…
Benny
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Probe a simple equation

$L$ is the side of a square, and it is 10cm. In the exercise I have a square shape which is cut with a semicircle in the bottom, and the radius of the semicircle is half the side of the square. I need steps to prove that $\displaystyle\frac{\pi…
JorgeeFG
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