Questions tagged [area]

Question 1

In rectangle $ABCD$, points $P$ and $Q$ lie on sides $AD$ and $DC$ respectively, such that $AP = 2 \times DQ$. Given that $AB = 5\,\text{cm}$, $BC = 10\,\text{cm}$, and the area of quadrilateral $BPQC$...

Question 2

This is the question that was asked in a competitive examination(NMTC) in INDIA,this question is from geometry.. I don't know how to go about solving the problem..In a $38\times 32$ rectangle $ABCD$, ...

Question 3

Hello, I am currently revising for entrance exams at a sixth form and this question has come up on one of the past papers I have spent a while looking at it and even asked a maths tutor but I cannot ...

Question 4

Let the coastline be the open arc of the unit circle between polar angles $0$ and $\phi$ (so its length is $\phi$). For a fixed free-arc length $s>0$, and for each pair of endpoints $A,B$ on this ...

Question 5

I apologize for an extremely vague title; I had to shorten it due to the character limit. Background We had this problem in a lecture on applications of definite integrals: If the area bounded by $y=...

Question 6

One possible approach to defining the surface area of a smooth 2D surface embedded into 3D Euclidean space, which is a natural generalization of the idea of calculating the arc length of a 1D curve as ...

Question 7

From what I've seen so far, the area function $A(x)$ of $f(x)$ is some antiderivative of $f$ such that $A(x) = \int_{a}^{x}f(t)dt$ and $A(x) = F(x) + C$. However, when I computed the area function for ...

Question 8

Let $ABCD$ be the unit square. $A(0,0,0),\; B(1,0,0),\; C(1,1,0),\; D(0,1,0)$ For $k\in[0,1]$, define $$ P(k)=(k,0,0),\qquad Q_0(k)=(k,1,0). $$ Now rotate the top edge $CD$ by an angle $\theta$ around ...

Question 9

The figure is an irregular pentagram in which the areas of the outer triangular sides are given. The area of the central pentagon is asked . My attempt : I tried to work in a repere to find the ...

Question 10

Five squares are drawn next to each other, as shown in the diagram below. If the area of each smallest square is $30 \text{cm}^2$, what is the area, in $\text{cm}^2$, of the shaded triangle? I'm not ...

Question 11

Both the curves meet at $\pi /8$ Beyond $\pi /8$, $y=\cos^2(4x)$ is completely above the $x$-axis until $x=\pi /4$, whereas $y=\cos(4x)$ is completely below the $y$-axis. I can calculate area up to $\...

Question 12

I recently posted a related question at Using GCF to Prove Pick's Theorem, but I accidentally intended the converse. Instead of revising a mostly coherent post, I'm making a new one with the backstory ...

Question 13

I am teaching high school geometry and I'm building between Euclid's number theory and his geometry. I want to prove Euler's formula in multiple ways, for much the same reason that Bonnie Stewart ...

Question 14

We're attempting to validate the CAD system surface area calculations. We can't seem to get the value that the CAD system is providing for the fillet surfaces on a screw head. (CAD A $= 14.27$mm$^2$) ...

Question 15

$O$ is a fixed point inside a square. Two perpendicular straight lines passing through $O$ intersect the sides of the square at four points, thus forming a quadrilateral inscribed in the square as ...

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Questions tagged [area]

Find the length of the side DQ

Find the maximum area of rectangle $PQRS$ [closed]

How would I go about solving this shaded area problem including a semi-circle resting on the diagonal of a 2:1 rectangle and touching the edges [closed]

Maximize the area enclosed by a fixed-length arc and a circle (endpoints of the arc may slide along the circle)

Show that the area bounded by a line and a conic is minimum if the line is parallel to the tangent to the conic at a "special point"

Does requiring that the triangles in a surface triangulation become small avoid the Schwartz lantern problem?

Why the area function of $\frac{1}{x^2}$ isn’t the same as its antiderivative?

Monotonicity of the surface area of a twisted square as a function of rotation angle

What is the area of the central pentagon in this irregular pentagram?

Five squares are next to each other. What is area of the shaded triangle?

Find the area of the region bounded between the curves $y=\cos(4x)$ and $y=\cos^2(4x)$ and between the vertical lines $x=0$ and $x=\pi /4$.

Using GCD to Prove Pick's Theorem

Using GCF To Prove Pick's Theorem [duplicate]

Surface area calculation of a screw head fillet

Can we prove this constant area ratio more simply?

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