2) a square with diagonals of length x
The diagonal cuts the square into two congruent right triangles.
The diagonal forms one side of the triangle. The other two sides are also the sides of the square, so they are equal.
The angle between the two equal sides is the same angle as an edge of a square, so it's 90 degrees.
Let a = length of a side of square. By pythagoras,
Now area of square is
Now try some for yourself. Here are some hints:
5) Equliateral triangle= 3 sides equal and all interior angles are 60 degrees. An easy way is to use the formula . But you can also split the triangle into two isoceles triangles are use pythagoras as in question 2).
6,7,8) I dealt with the method to solve these in part in my explantaion in 2).
9) the ratio 3:4:5 is a pythagorean triple (i.e. they form the sides of a right angle triangle)
10) Any polygon (including hexagons) can be cut into triangular pieces.