Determine the total shaded area of the 'kissing triangles'.
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
Take a ten-sided die (or other random number generating tools - a pack of cards with the picture cards removed, a calculator, a phone app...) and generate three numbers. Construct a triangle using these three numbers as the side lengths.
If you're not sure how to use a ruler and compasses to construct a triangle given the lengths of its three sides, watch the video below:
Generate a few more sets of numbers and draw some more triangles.
What do you notice?
Here are some questions you might like to consider:
Here is a game you could play:
Start with 10 points. Roll three dice. If a triangle can be drawn, you gain a point, if it can't, you lose a point. If you reach 20 points you win the game, if you reach 0 you lose.
Which is the more likely result?
Here is a game you could play with another person:
Player A chooses an integer length between 1 and 10cm. Player B randomly generates the lengths of the other two sides. If a triangle can be drawn, Player B wins; otherwise they lose.
Is there a "best" length that Player A should choose?
Is this a fair game?
Now explore what happens if you generate 4 numbers and draw a quadrilateral.