Area of Regular Polygons

Formula 1:

The a in the formula stands for apothem. the apothem is the perpendicular segment for the center to the side of the polygon

The p stands for the perimeter of the polygon

The A stands for the area of the entire polygon

Formula 2:

A= 1/2 nas

The n stands for the number of sides in the polygon

The a stands for the apothem

The s stands for the lenght of a side


Example:

1) A pentagon had an apothem of 3 inches. If a side measures 15 inches find the area

Formula 1:                                                                           Formula 2:
A=1/2 ap                                                                              A=1/2 nas
A= (1/2) (3) (75)                                                                  A= (1/2) (5) (3) (15)
A= 112.5 squ. in                                                                  A= 112.5 squ. in


You Try:

1) Find the area of a hexagon with an apothem of 6 and a side measuring 13

2) Find the apothem of a pentagon with an area of 115 and a perimeter of 5



Compositions of Transformations

In compositions of transformations the first step you do is the second transformation they give you. Then the first one they give you is the second one and your final answer. 

Example: Given point A(−2,3). State the coordinates of the 

image of A under the composition T(−3,−4)r x − axis

Step 1: When reflecting over the x-axis the you negate the y-value.

(-2,3) -----> (-2,-3)

Step 2: Using the new point created move the point left and right following the rule.

(-2,-3) ------> (-2+-3, -3+-4) -----> (-5,-7)

Final Answer: (-5.-7)

Questions:

1) Given Point A(5,3)find the transformation r x−axis r y=x

2) Given the point A(-8,-10) find the transformation   r x−axis r y−axis