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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Triangle with two sides given find the greatest area if the area is prime number

A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is n square centimeters, where n is a prime number. What is the greatest possible value of n? (A) 11 (B) 12 (C) 19 (D) 23 (E) 24
Hrach Sahakyan
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Proof of area function equals antiderivative anomaly

In my math textbook they have a proof that an antiderivative to f(x) is the same as the area function to f(x). They assume that f(x) is continuous and that f(x) is a growing function. By looking at the pictures above and drawing some rectangles…
Carl
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Finding the width of a smaller rectangle

We have a large rectangle, with a width of 14m and a length of 9m. In the middle of this rectangle is a smaller one, with a length given of 5m. The text prompts me to use the width of the larger rectangle, subtract a certain number from it to…
Ryland04
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How to find the area of the rectangular region 2 ≤ x ≤ 5, -1 ≤ y ≤ 3

How to find the area of the rectangular region $2 ≤ x ≤ 5$, $-1 ≤ y ≤ 3$. I tried to plot the graph in $xy$-plane, but I'm not sure how to find the area.
VinuKumar
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Least Area bounded

Area bounded by f(x) = $x^3/3$ - $x^2$ +a and the straight line x=0, x=2 and the x axis is minimum. Find a This is the screen shot of the function when a=0.6. Scrolling the value of "a" from 0 to 9, I am finding the function to have least value…
Scáthach
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Find area of the fourth triangle given the area of three triangles.

This is the question that I got in TCS Ninja under the Quantitative section. How shall I do this? Help !!
asn
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How do you calculate area of two circles joined by tangent lines

please can you help to provide the mathematical steps required to calculate the area of a shape formed by two circles of different diameter joined together by two tangential lines.
Karl Whopples
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Find the length of x for an arrow head

I am struggling to get some traction on this and need someone to show me how to calculate this. I have a GCSE question that asks: In the attached image I'm being asked the following: The arrowhead has an area of $3.6cm^2$. Find the length $x$.
Dan
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Area of combined shapes

Is it really possible to get the area of the shaded part below because i have tried to divide the figure into several parts but my answer comes to 7.85cm².please someone help me solve it.
Makau Elijah
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How to compute the area on top of this red green line?

https://en.wikipedia.org/wiki/Gini_coefficient I says that if u people own f portion of the wealth, then the gini index is f-u. They draw some triangle there It seems that the area on top of the green line and to the left of the red line is simply…
user4951
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Minimum area of region bounded by a thread

Suppose you have a thread of length $l$ and 4 thumbtacks located at $(1, 0), (0,1), (-1, 0), (0, -1)$. You have to make closed region with the thread so that all the 4 thumbtacks lie inside the region such that the area bounded by the thread is…
B2VSi
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Measure of overlap of plane figures

Do you know if there is any measure which quantifies how much two different plane figures overlap? if $A_1$, $A_2$ denote the areas of figure $1$ and $2$ respectively, and their overlap area is $A_{\text{over}}$, then the measure $d$ can be define…
Caute
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How to find the surface area of a cylinder given only diameter and length?

The exact question is, "Your Siberian Husky, Emma, and her Husky-Shepherd friend, Luca, destroy your fence pickets in the backyard. To repair the fence, you buy new pickets and galvanized nails with a diameter of 1.9 mm and a length of 5.6 cm.…
Kei Haruki
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How can the area of a square be less than its length?

The area of a square is calculated by squaring its length. For example, a square with a length of $2m$ yields an area of $4m^2$. However, if a square has a side length of $1mm$, then its area is $1mm^2$. In other words, it has a length of $0.001m$…
user552217
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calculating the surface of an irregularly shaped vessel by knowing its volume

Is it possible to calculate the surface area of an irregularly shaped vessel, like a laboratory volumetric flask, by knowing its volumen? By knowing how much liquid it can hold, one could use the formula for the surface area of a cylinder and find…
Ricardo
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