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 find the area of the slice of a circle?

Let us have a circle of radius $1$, which is placed on $X$-$Y$ plane. The center of the circle is at $(0.5,0.5)$. If I cut a slice of the circle at $x=0.3$, how to find the area of the slice? Is there a formula which is a function of $x$ and radius?
Dimitrios
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If the lateral surface area of a square-based pyramid with equal edges is $144\sqrt{3}$, what is the area of the base?

The lateral surface area of a square based pyramid having equal edges is $144√3$ cm^2. Find the area of base. My Attempt: let, length of base =$a$ slant height=$l$ Then, $$L.S.A. of pyramid=144√3$$ $$2al=144√3$$ $$al=72√3$$. Then, what should I do…
pi-π
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Decide if a point is inside quadrangle

Let's say computer randomly generate 4 points on canvas. points are A[x1,y1] B[x2,y2] C[x3,y3] D[x4,y4] I need to decide if a point P [x,y] is insided the area built by the 4 points. the 4 sides are AB, BC, CD, and DA. I can compare the areas if…
Di Wang
  • 511
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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 AC 37.8ft; BD 50.6 I have used this formula to find the area I got 950sq.ft as the answer. When I try to check in…
GopsAB
  • 21
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How to find area of remaining square with shapes inside

Pretty much there is a square with a height and width of $2$", inside there is a perfect circle with radius $1$". Also overlapping the circle and square is a isosceles triangle also with height $2$" and width of the bottom to be $2$". (Truly to see…
porter
  • 21
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Formula to find the area in relation to changing lengths of a square

If you double the side length of a square, how many times bigger is the area of the square? How many times bigger is the area if you triple the side length? What about if the side length is ten times as big or half as big? Generalise this concept…
Aaliyah
  • 21
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Combined overlap area question

I'm having a bit of trouble with this question: Sue works in a rug shop. She as three rugs with a combined area of $200 m^2$. She arranged the rugs so they overlap and cover a floor area of $140 m^2$. The total floor area that is covered by exactly…
numbermaniac
  • 248
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i need to know the formula for the surface area of a disk

I am trying to figure out a questions but i need to know the formula for the surface area of a disk. if anyone could help me out it would be great. The question i am trying to answer is: " the concrete pipe shown in the diagram has the following…
samantha
  • 31
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Polygon area problem

How can i calculate area of that kind of polygon. I know the coordinates of all vertices. I apply Shoelace formula, but it gives me wrong value then expected. Autocad application calculates true value. How can it calculates. What is the correct…
moleschott
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Find value of area of semicircle cross-sections for the lines $x+2y=8$, the x-axis, and the y-axis

The base of a solid is a region in the $1st$ quadrant bounded by the x-axis, the y-axis, and the line $x+2y=8$. If the cross-sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid? Area of a semicircle:…
user159778
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Regular Octagon Area

Doing some maths homework I came across the area of a regular octagon on Google. This was given by: $$ A=2(1+\sqrt{2})a^2 $$ I thought this looked rather ugly and slightly complicated and so began to look at regular octagons myself (Yes, I'm a nerd…
kettboy
  • 27
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floor plan optimization?

I have sheets of mesh $7.05\text{ m} \times 2.62\text{ m}$. I have a floor area of $17.5\text{ m} \times 24.5\text{ m}$. What is the best way to calculate optimal laying/orientation of mesh? If someone can advise the mathematical theory I can…
pablorenato
  • 11
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Finding an area of the farm in cm2 on the map

So the area of the map is 2000 hectares but the question is asking to find the area of the farm in cm2. I'm a bit confused as how to work this out. I know that 1 hectare is equals to 10,0000 m2. The scale of the map is 1: 180,000
lase
  • 61
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A silly question regarding square meters

Suppose we have two areas: $B$ of size $4m^2$ and $A$ of size $2m^2$. What is the ratio between their sizes? A simple division would yield 2, but I think that the answer is 4, as illustrated below: Could you please clear up the confusion? (E.g. in…
user167425
  • 19
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Ambiguous Limits in Area Determination

I am to find the centroid of the area bounded by the curve $y=8x^3-24x+11$, the $x$-axis and the line $x=-1$. Now I know that the centroid requires me to find the area under the curve first. I have run into a snag in that this curve intercepts the…
Medrine Nyamao
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