Use 30-60-90 and work backward through the triangles

2. Given Circle S with TV = 8, find the area of the circle.

Use 45-45-90 and the area of a circle formula.  TU = So the radius must be half 

3.  Given WXZY is a trapezoid with WX = WY = 10, find the length of XZ .

Use 45-45-90  ans.  10 +

4.  Given RHOM is a rhombus, with HM = , find the perimeter of the rhombus.

  Use 30-60-90  The perimeter is 4(12) = 48

5.  Given the regular octagon as shown, find the length of ET, if ER = .

Divide the octagon into 45-45-90 triangles and rectangle 
Note the length of ET = 12 +   These cannot be combined. 

6.   Given a square pyramid with the perimeter of the base of 72 and height of 12, find the length of the slant height.

Use the Pythag. theorem on the central triangle. 

8.  An equilateral triangle has a perimeter of 6.  Fid the length of the altitude.

Drop a perpendicular to represent the height.  The triangle formed is a 30-60-90 since the three angles of an equilat. tri. are 60 each.  The length of each side is 2 since the perimeter is 6 and each side must be the same.  Use the 30-60-90 to find the side opp. the 60 degree (1/2 hyp x )

6

10.  Given the cube as shown, if GF is  6 and M is the 
        midpoint of , what is the length of ?

I had this answer wrong last night.  Recheck.  My mistake. 

Introduce GC and find its length using 45-45-90.Since GC is so is AC and MC will be half or .  Since GC is the hypotenuse of triangle GCM use the Pythagorean theorem to find the length of GM.