# Questions tagged [area]

Area is a quantity that expresses the extent of a two-dimensional measurement of a shape.

2,961 questions
Filter by
Sorted by
Tagged with
35 views

### Area bounded by $f(x) = -2(x-3)(x^2+1)$ and $g(x) = ax$

I have the following equations and trying to determine the value of a $g(x) = ax$ $f(x) = -2(x-3)(x^2+1)$ Hello, I am trying to identify the unknown value of a > 0 such that the following holds: ...
49 views

85 views

### Finding the area under the inequality $\sin^2 \pi x + \sin^2 \pi y \le 1$ for $x,y \in [-1,1]$

Find the area under the inequality $$\sin^2 \pi x + \sin^2 \pi y \le 1 \text{ for } x,y \in [-1,1]$$ I coudn't do this problem without using a graphing calculator: It's easy to see now that in each ...
20 views

### Calculate the dual basis and tangent basis vectors

A coordinate system with the coordinates s and t in $R^2$ is defined by the coordinate transformations: $s = y/y_0$ and $t=y/y_0 - tan(x/x_0)$ , where $x_0$ and $y_0$ are constants. a) Determine the ...
43 views

### Area of triangle under tan conditions.

For an acute triangle $ABC$, the following conditions hold. $$\frac{1}{\tan A} + \frac{1}{\tan B} + \frac{1}{\tan C } =2$$ $$a^2 + b^2 + c^2 =50$$ Compute the area of such a triangle. I used a tan ...
70 views

### $A,B,C$ and $D$ are concyclic.$AC$ is the diameter of the circle and $AD=DC$.The area of quadrilateral $ABCD$ is $20cm^2$.

$A,B,C$ and $D$ are concyclic . $AC$ is the diameter of the circle and $AD=DC$ . The area of quadrilateral $ABCD$ is $20c$m$^2$. Draw a line $DE$ such that $E$ is a point on $AB$, and $DE$ $\bot$ $AB$....
60 views

### Is there a geometric intuition for division of area by length?

To give you the context of this question, before I had a question about why an area of a square equals to its side squared, and how to see it geometrically, because multiplying a length by a length to ...
68 views

### The plane $𝑥/4+𝑦/4+𝑧/7=1$ intersects the $𝑥-$ , $𝑦-$ , and $𝑧$- axes in points $𝑃, 𝑄, 𝑅$. Find the area of the triangle $Δ𝑃𝑄𝑅$.

The plane $𝑥/4+𝑦/4+𝑧/7=1$ intersects the $𝑥-$ , $𝑦-$ , and $𝑧-$ axes in points $𝑃, 𝑄, 𝑅$. Find the area of the triangle $Δ𝑃𝑄𝑅$. So here's my attempt. First I find the normal vector:...
29 views

### Finding the length between the two vertices of two different triangles having the same base side and same perimeter by a shorter method.

My approach:- Using distance formula I found the lengths of AC,CB and AB. Using them I found out the perimeter of triangle ABC and it came out to be 18 square units. Hence, $$AB+BC+CA=18 units$$ ...
289 views

### Integral Calculus, Infinitesimal

To integrate $y=f(x)$ from $a$ to $b$ we break the function into small rectangles of width $dx$. So the $n$-th rectangle will be at a distance of $n\,dx$ from $a$ on the $x$-axis. Let there be $t$ ...
90 views

### How do I use cross products to find the area of the quadrilateral in the $𝑥𝑦$-plane defined by $(0,0), (1,−1), (3,1)$ and $(2,8)$?

How do I use cross products to find the area of the quadrilateral in the $𝑥𝑦$-plane defined by $(0,0), (1,−1), (3,1)$ and $(2,8)$? So what I first do is find two vectors. Gonna use (0,0) as ...