square on the top of a square

Question

i am stuck with a question of mensuration for three days and i posted it on facebook and asked friends but no correct solution yet. please help .

How far have you gotten? Did you , for example, manage to determine $PQ$ at least? — Sarvesh Ravichandran Iyer, Jul 09 '18 at 07:45
Please show us how far you've come with your own attempts; MSE is not "Do-My-Homework Central". — Acton, Jul 09 '18 at 07:53
@астонвіллаолофмэллбэрг yes. that is radius multiplied by square root of 2 — Vindhyachal Vindhyachal, Jul 09 '18 at 08:02
i am having difficulty in determining the area of small region between the square and the circle — Vindhyachal Vindhyachal, Jul 09 '18 at 08:03
The length of the side of the small square is immediate from Pythagorean theorem. How come you didn't try it? — Ennar, Jul 09 '18 at 08:09
@Ennar thanks. can u tell me how to find the area of the small region between the circle and the smaller square? — Vindhyachal Vindhyachal, Jul 09 '18 at 08:16

score 2 · Answer 1 · answered Jul 09 '18 at 08:06

2

$(14+a)^2 + (a/2)^2=(14*2^{0.5})^2 $ From geometry...

answered Jul 09 '18 at 08:06

Pi_die_die

107
6

This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review – Taroccoesbrocco Jul 09 '18 at 09:04
@Taroccoesbrocco, yes it does provide an answer. – Ennar Jul 09 '18 at 11:47

score 1 · Answer 2 · answered Jul 09 '18 at 07:51

1

You must have $|XY|=2\cdot(|WX|/2)$, which is

$(\sin(v)-\sin(45))\cdot14\cdot\sqrt{2} = 2\cos(v)\cdot14\cdot\sqrt{2}$

Which you can solve for $v$ and substitute back into $|XY|$. Then the area is $4|XY|^2$.

answered Jul 09 '18 at 07:51

Oppenede

546

which angle is v here ? – Vindhyachal Vindhyachal Jul 09 '18 at 10:29
@VindhyachalVindhyachal Angle of OX relative to x-axis – Oppenede Jul 09 '18 at 17:51

score 1 · Answer 3 · answered Jul 09 '18 at 08:00

1

Hint: Use symmetry and the Pythagoren Theorem for $\triangle AOT$, where $O$ is the center of the circle and $T$ is the intersection between $AB$ and the line through $O$ perpendicular to $AB$.

This directly gives you everything you need

answered Jul 09 '18 at 08:00

asdf

4,587

square on the top of a square

3 Answers3