Questions tagged [area]

Area is a quantity that expresses the extent of a two-dimensional or three-dimensional surface or shape.

2,235 questions
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Finding the area between two regions in the plane

I have two regions, given by $y>\sqrt{2}x - \frac{1}{4x}$ and $y< \sqrt{2}x + \frac{1}{4x}$. How can I find the area of their intersection? If their is no easy analytical way, could someone ...
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Ratio between the areas of two rectangles inscribed in a triangle and the area of the triangle

Let's denote $A(X)$ the area of the polygon $X$. Let $S$,$R$ be rectangles inside a triangle $T$. Find the maximum value of: $$\frac{A(R)+A(S)}{A(T)}$$ My try The only property i know (from a ...
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Find the area bounded by a quartic curve

Find the area bounded by the curve defined by: $x^4+y^4=x^2+y^2$ . The final solution should be $\sqrt{2}\pi$. I tried to change it into polar coordinates, but I couldn't calculate the integral.
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Area Inside A Loop Formed By Parametric Equations

We are given: $x=49-t^2$ $y=t^3-16t$ The curve apparently makes a loop which lies along the x-axis. I need help finding total area inside the loop. I don't know where to even start. If it helps, ...
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Area between curves.

I have to calculate area bounded by curves : $(x^3+y^3)^2=x^2+y^2$ for $x,y \ge 0$. I tried to use polar coordinates, but I have : $r^4(\cos^6\alpha +2\sin^3\alpha\cos^3\alpha + \sin^6\alpha)=1$
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Help me to calculate polyhedron area or let me know the references about it.

I'm a student who is studying the Management Science in the Republic of Korea. I'm looking for a reference to calculate the area of the system of inequalities. I can easily calculate when the number ...
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Why does $\int_0^R 2 \pi r \,\mathrm d r$ give the area of a circle?

There's a method of computing the area of a circle by dividing it in concentric rings with infinitesimal width. Let $R$ be the radius of the circle and $r$ be the radius of the rings. The area of the ...
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Prove the equality of circle's areas

Through a random point inside the circle, we draw $4$ lines with $45$ degrees between each other. Prove, that the total area of odd pieces, equals total area of even pieces. I suppose there is a ...
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Triangle problem, $AC=3$ , $AB=5$ ,…, then $PH=?$

In $\triangle ABC$ : $AC=3$ , $AB=5$ , $\angle ACB= 90 ^ \circ$, $P$ is a point inside $\triangle ABC$ such that $PA+BC=PB+AC=PC+AB$, $H$ is a point on the line $AB$ such that $\angle PHB=90^\circ$ ...
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unable to understand tan/arctan-related integral transformation

I'm currently studying area between curve and x axis on Khan Academy. I understand that the But I am puzzled by how did we get to this step from the previous step?
Given that $[ABC]$ : Area of small circle = $\frac{3\sqrt3}{4}$ : $\pi$. How many parts of area of small circle is inscribed in large circle? [closed]
In the common region of two circle, $\triangle ABC$ has been drawn with its maximum area such that the proportion of the maximum area of $\triangle ABC$ and the area of small circle is equal to \$\frac{...