Derive a formula for finding the area of any kite.
A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?
Mathematics has always been a powerful tool for studying, measuring and calculating the movements of the planets, and this article gives several examples.
12 x - x = 11 x
11 x = 2 right angles = half an hour
Since 12 x is equal to the time passed,
12/11 * 30 minutes = 32 8/11 minutes.
It will be 32 8/11 minutes before they are at right angles
Thank you Chin Siang (Tao Nan School,
Singapore) for this splendid solution in HTML and the excellent
James sent a good solution too and he
makes the comment "I had to keep reminding myself that every
time the big hand moves so does the little one."
Here is the solution from the Strabane Grammar
School Key Stage 3 Maths Club:
We got a clock and set the hands to 3 o'clock i.e. at
We moved time forward and noticed that the hands got closer,
were on top of each other, and then separated, the minute hand
moving in front, until they were at right angles again between 3.30
We tried to calculate the time more precisely. Every minute the
hour hand moves forward 0.5 degrees and the minute hand moves
forward 6 degrees so the angle separating the hands will change by
Since they have to close up and then separate again this will
take 180/5.5 minutes i.e. 32 8/11 minutes. After another
32 8/11 minutes the hands will be perpendicular again.