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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What is the smallest possible area for a triangle of integral side lengths whose perimeter is 15cm?

What is the smallest possible area for a triangle of integral side lengths whose perimeter is 15cm? Round your decimal answer to the nearest hundredth. How do you find this?
Mike Weng
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Area bounded by two curve and the line $x=0$ and $x=\frac{\pi}{4}$

The area of the region between the curves $y = \sqrt {\frac{{1 + \sin x}}{{\cos x}}} $ and $y = \sqrt {\frac{{1 - \sin x}}{{\cos x}}} $ bounded by the lines $x=0$ and $x=\frac{\pi}{4}$ is (A) $\int\limits_0^{\sqrt 2 - 1} {\frac{t}{{\left( {1 +…
Samar Imam Zaidi
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How does a defect rate scale with the area of a wafer?

this is my first time posting here so hopefully I'm not breaking any rules. I have a fairly simple question but I can't seem to wrap my head around it. I'm currently reading "Computer architecture: A quantitative approach" and in chapter 1 the…
Hayden
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Finding the maximum area of a rectangle

I'm having trouble with this problem and I need help to solve it... A person has $800$ ft of fencing. He wishes to form a rectangular enclosure and then divide it into three sections by running two lengths of fence parallel to one side. What should…
Apex Raider
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Given a fixed perimeter, which shape will have the minimum area?

I understand that a circle will have the largest area for a given perimeter but I don't get The smallest area. Is it a triangle because it has the least amount of sides so must be smaller?
Plasman
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Is a line segment non measurable or has 0 area?

My problem is the following: Let's take a line segment. Question is, does it have an area (2D Jordan measure)? I think it has $0$ area, because we know that $\emptyset$ has $0$ area, and if we construct a sqaure with sidelength $\delta>0$, which…
math_inquiry
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In the isosceles triangle, the two squares (white) both have an area of four. Find the area of the shaded.

In the isosceles triangle below, the two squares (white) both have an area of four. Find the area of the shaded. According to my answer key, the answer is $9\sqrt{2}$ square units. How can I show the solution through the parallel line theorem?
AYA
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Finding ratio of area of triangle and area of trapezium

Can anyone help me with this? --> Image I already answered a, b, c i) and c ii) but how am I supposed to do c iii)? I'm quite confused and I don't know how to solve this particular question.
SynergyBoi21
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Calculate the number of elements to cover an area within a specific distance

What is the minimum number of items we need to place in an area of 10000m2 and a distance of 5 meters with the whole area covered?
Berhanu Abebe Dagnaw
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Find area of a seven-point star inscribed in a circle of radius 1

I need to know area of the 7 point star and radius of the circle is 1.
Graph Patula
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How to calculate the area enclosed by an implicit function?

I want to calculate the area bounded by the region $y^3 - x^4 - y^4 = 0$. What can I do with this? Thanks for any help.
mahisafa82
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How would you go about finding the area probability?

A triangle is formed inside a square by joining corner C with the mid points of sides AD and AB. If a point in the square is chosen randomly, what is the probability that the point will be inside the triangle as well? The answer is 37.5%. However,…
orangebull
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Finding the area of the region bounded by $x=0$, $y=0$, $2x^2=\sqrt{x^2+y^2}$, $2y^3=\sqrt{x^2+y^2}$

I have 4 equations and need to find the area bounded by the corresponding curves. I don't know how to approach it.
ERJAN
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Area of the shaded region- Rotating Wheel

I wanted to compare answer for area of the region in the middle of the square, the leaf sort of shape. So the circle is like a wheel and as it turns to the other side, it basically draws the upper half of the leaf and same process with the lower…
mathsiscool
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Getting the AREA of an OIL SPILL

How much area in $m^2$ will $200 cm^3$ of oil cover if it forms a layer of $35mm$ thick? i dont know what formula i will be using, my teacher never discussed this and i cant seem to find any on the internet, thanks.
Daimler
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