How do i simplify sinxcos^2x+sin^2x

Mickey needs to cut pieces of ribbon that are each 1 meter long tie onto balloons. if he has 8 pieces of ribbon that are each 1 dekameter long. how many 1 meter pieces of ribbon can he cut

The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.