Consider the pentagon  How many non-overlapping triangles can an n-sided figure be split into?

How many diagonals does a hexagon have? (Note: A hexagon is a 6-sided / 6-corner polygon shape and a diagonal is a line segment connecting two non-adjacent corners.)

Yvonne wants to use a dissection argument to justify the formula for the area of a circle. She dissects the circle into congruent sectors and reassembles the sectors as a parallelogram–like figure. The diagram below shows the arrangement for a circle dissected into 8 sectors. Yvonne knows that as the number of sectors of the circle increases, the reassembled figure becomes closer and closer to an actual parallelogram so that it can be used to determine the area of the circle. Determine the value of each characteristic of the parallelogram in the table below. Select the best value for each characteristic

a. Find the lengths of the sides of a rectangle whose perimeter is 40 cm and whose area is 75cm². (Perimeter refers to the sum of all the sides). b. Find two succesive natural numbers whose sum of squares is 13.