All Questions
484
questions
-2
votes
0
answers
22
views
Finding the area of a triangle knowing the coordinates of the midpoints of its medians [closed]
The midpoints of the medians of $\triangle ABC$ are $(1,2)$, $(4,4)$, and $(2,8)$. Find the area of the $\triangle ABC$.
2
votes
0
answers
33
views
What is the maximum area of n non-overlapping equal area triangles inscribed in a circle of radius
What is the maximum area of n non-overlapping equal area triangles inscribed in a circle of radius 1?
For n = 1, the triangle is equilateral.
For n = 2, we have 2 isosceles right triangles sharing a ...
- 21
3
votes
4
answers
174
views
Area of the triangle inside the triangle
Area of each shape in the triangle is written. What is the area of the
shaded region?
Based on my search, $\dfrac{S_{\triangle MNP}}{S_{\triangle ABC}}$ can be calculated by Routh's Theorem. assuming ...
- 6,794
5
votes
2
answers
174
views
Area of tight-angled $\triangle POB$ given extensions of $OP,BP$ to circle centred at $O$ through $B$?
We have a triangle $(\triangle POB)$ within a semicircle. $OP$ and $BP$ are extended to $OA$ and $BQ$. $AP = 5$ and $PQ = 7$. What is the area of the triangle?
It's a problem I stumbled upon on ...
- 53
3
votes
4
answers
803
views
A right-angled triangle has sides of integer length. Its area (in square metres) is twice its perimeter (in metres). What are the lengths of the sides
A right-angled triangle has sides of integer length. Its area (in square metres) is twice its
perimeter (in metres). What are the lengths of the sides?
The equations I have made so far is:
Using ...
- 59
0
votes
1
answer
37
views
Knowing that the area of a lateral face is equal to the area of the base, find the measure of the angle formed by the planes $(MBN)$ and $(ABC)$.
the question
Let $VABCD$ be a regular quadrilateral pyramid, $M$ the midpoint of the edge $VC$, $N$ the midpoint of the edge $AD$. Knowing that the area of a lateral face is equal to the area of the ...
- 748
7
votes
3
answers
290
views
Maximizing area of the triangle in a quarter circle
The radius of the quarter circle is $6\sqrt 5$ and we assume that $OA= 5$ and $OC=10$. What is the maximum area of the blue triangle?
Interpreting the problem statement, I believe that points $A$ and ...
- 6,794
1
vote
1
answer
73
views
Area of a triangle in Lockhart's Lament
In the essay Lockhart's Lament (page 4), the author describes a proof for the standard area of triangle $(bh)/2$ by enclosing the triangle in a rectangle and chopping the rectangle into two (perhaps ...
- 185
25
votes
3
answers
800
views
What's the area of the triangle in this geometry problem? I think I can solve it, but it's way too convoluted...
I am trying to solve this geometry problem from an exam. The exam is supposed to be 3 hours long, and this is supposed to be 1 out of 10 problems. So given that, the solution should be something ...
- 1,107
20
votes
2
answers
773
views
What is the expected area of a triangle in which each side is a random real number between $0$ and $1$?
Let $a,b,c$ be three independent uniformly random real numbers between $0$ and $1$. Given that there exists a triangle with side lengths $a,b,c$, what is the expected area of the triangle?
Using ...
- 25.8k
0
votes
1
answer
166
views
How to find the area of the given circle?
Given, we have an $\square ABCD$ with a side length of $1\text{cm}$. We construct its diagonal $AD$. From $C$, we draw the altitude $CE$ of $\triangle ACD$. Now, we construct the altitude $FE$ of the ...
1
vote
2
answers
106
views
Surface area of sphere coming out as $\pi^2 r^2$ [duplicate]
Take a hemisphere and divide its surface area into strips like on a watermelon.
Each strip can be approximated as a triangle with the long two sides = $\pi \frac r2$ (quarter of circumference) and if ...
- 19
3
votes
3
answers
117
views
Find the area of BGHF
This problem is taken from the Chinese WMTC 2019 Junior Division.
If ABCD is a square of area 40, and $BE=\frac{1}{3}AB, BF=\frac{2}{5}BC$, find the area of BGHF.
I tried using the idea of area ...
- 163
2
votes
2
answers
99
views
Find the area of the quadrilateral $ABDC$
If $A=(2,1), B(8,1), C(4,3), D(6,6)$ then find the area of the quadrilateral $ABDC$.
My Attempt:
Area of quadrilateral= area of triangle ABD + area of triangle ADC.
Area of triangle ABD= $\frac12|2(1-...
- 8,338
0
votes
0
answers
48
views
How to prove $EN=\dfrac{AI}{2}?$ and $KN=\dfrac{CJ}{2}$? and $\dfrac{Area(ABD)}{2}+\dfrac{Area(BCD)}{2}=\dfrac{Area(ABCD)}{2}$?
Given
\begin{aligned}
\operatorname{Area}(E F G H) & =E K \cdot F G \\
& =(E N+K N) \cdot \frac{1}{2} B D \\
& =\frac{1}{2} B D \cdot E N+\frac{1}{2} B D \cdot K N \\
& =\frac{1}{4} ...
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