# Questions tagged [area]

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

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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.
1answer
75 views

### How do I calculate?

How do I calculate cross-sectional area of this: ${r}=\sqrt{sin\theta} \,$, when $0 \le \theta \le \pi,$ Don't know what is the right answer but I have get that the area is 1. Is that right answer?...
1answer
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### How do I calculate area?

How do I calculate the area of this: $D=\{ (x,y)\mid 0 \le x \le 1, x^2 \le y \le x^2+2 \}$ ${A}=\iint_D \, \textrm{d}A.$ Don't know what is the right answer but I have get that the area is 6. Is ...
1answer
48 views

1answer
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### Finding enclosed area

Hints only please !! I gave a test today, and it was asked to find area enclosed by the curve $x^4 + y^4 = 2*x*y$. This is an implicit function. A quick obs. shows me that, the curve is entirely bound ...
3answers
27 views

### Under between the x- and y-axis of the graph of $y=x^n$

Consider the graph of $y=x^n$ for $n>1$ and $x>1$. The area bound between the curve and the x-axis between $1$ and $a$ is one third the area between the curve and the y-axis between the values ...
0answers
37 views

### How to formally prove this integral identity?

I was doing some investiations into 'areas under curves' an found by a geometric analogy the following integral identity: $$\int_0^a f(x)dx =\frac12 \int_0^{f ′ (a)} (a- f^{-1}(f′(x)))^2 dx$$ ...
2answers
70 views

### Finding out the value of $\angle DQC$ in a trapezium $ABQD$ where $\angle DCB$ = 30$^\circ$

In this below diagram, $\angle ABC=60^\circ, \angle DCB=30^\circ$, $AD$ is parallel to $BC$ and $AP$ is perpendicular to $BC$. Both the area and perimeter of $ABCD$ and $APQD$ are equal . What is the ...
1answer
42 views

### Improper integral - Calculating Area of Floor Function

I'm stuck trying to calculate the area of the region defined by: $\begin{Bmatrix} {(x,y)\in\mathbb{R^2}:0\leq x\wedge 0\leq y\leq 2^{-\lfloor x \rfloor}} \end{Bmatrix}$ I'm just starting studying ...
3answers
46 views

### Area of a right trapezoid with bases $15$ and $8$, and height $9$

I can't figure out how they got that. I got 1080, they got 103.5. How???
1answer
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1answer
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### Calculate Overlapping Area of $2$-Dimensional Shapes

I am running a Computer Simulation where 2 Shapes are moving towards each other and will eventually overlap. I want to calculate the overlapping Area of the shapes - in this example a Circle and a ...
2answers
92 views

### Find area of quadrilateral in triangle. [closed]

What is the area of $HIJK$ quadrilateral, if the area of $ABC$ triangle is $70$, $BE=ED=DA$, and $BF=FG= GC$?
3answers
63 views

### Finding percentage increase of area [closed]

Find the percentage increase in the area of a triangle if its each side is doubled?since no information is given about the type of triangle in question, so should i take a equilateral or isosceles or ...
2answers
96 views

### Do the given perimeter and area corresponds to many shapes? [closed]

I have a perimeter P and area A of a planar shape. How to prove that there are many shapes that corresponds to those perimeter and area values?