Aim: How do we find the area of regular polygons?

Area of a regular polygon- The are of a regular polygon is n (number of sides) times a (apothem) times s (side length) divided by 2 (nas 1/2).







Fo example if a (apothem) is 6 cm long and the side (s) is 5 cm long the area of this hexagon would be
5 times 6 times 6, which equals 180 and then you divide 180 by 2. The are of this hexagon would then be 90 cm squared.




What would be the area of a pentagon with an apothem of 7 and a side length of 8?

Aim: How do we find the area of a circle?

Circle Area Formula- The area of a circle is given by the formula: pi times the radius squared.

So for example:




The area of this circle would be the radius (5) squared (25) times pi. You could solve this problem by typing it into a calculator or just leaving it in terms of pi, which would be 25 pi.



Solve the area of this circle:

Aim: How do we find the area of parallelograms, kites and trapezoids?

To find the area of a parallelogram is the same formula as finding the area of a rectangle:
Base times Height (b x h) = Area

• 

To find the area of a kite you must follow this formula:







(Diagonal 1 + Diagonal 2) / 2 = Area




To find the area of a trapezoid you must follow this formula:









(Base 1 + Base 2) /2  times Height = Area





Try these area problems:





If Diagonal 1 is 25 and Diagonal 2 is 30, what is the area of the kite?




If Base 1 is 6, Base 2 is 3 and the height is 8, What is the area of the trapezoid?




If the base is 7 and the height is 5 what is the area of the parallelogram?

Aim: How do we calculate the are of rectangles and triangles?

To calculate the area of a rectangle you must follow this formula:
 
Base times Height (b x h) = Area



To find the Area of a triangle you must follow this formula:

Base times Height times 1/2 (b x h x 1/2) = Area



Try these problems:
If the base of a rectangle is 7.3 and the height is 4, what is  the area?

If the base of a triangle is 6 and the height is 5, what is the area?

Aim: How do we find the locus of points?

The locus of points is the set of all points that satisfy a given condition.

To find the locus of points on a graph you would need to know the condition, for example;

What would the locus of points be 15 meters from Point P? Point P, from the theorem, is the stake to which Fido, the dog, is tied.  His leash is 15 feet long.  The path that Fido can travel at the end of his leash is "the locus of points". The locus of points at a distance of 15 feet from point P is a circle (with center P and radius 15).

In this image, Fido could move freely within the 15 meters of his leash, so any point at the end of his leash would satisfy the condition asked.

There are other conditions such as lines that can include a locus of points.
The locus of points for a single line would be two separate lines on the sides.
 For example what are the locus of points 3 cm from line L, would be the two red lines.

Try this: what are the locus o points from X=2?

Aim: What is a mathematical statement?

A mathematical statement is a statement that can be judged to be true or false.

Conditional- The conditional is the most frequently used statement in the construction of an argument or in the study of mathematics.

Converse- Reversing the first and second statements in a conditional.

An example of a Conditional: If you take a shower, than you smell good.
The converse of this statement would be: If you smell good than you took a shower.

Than there is the Inverse of a conditional.

Inverse- Formed by negating the hypothesis and conclusion.
The inverse of the conditional would be: If you don't smell good than you didn't take a shower.

Write the converse and inverse of this statement: If it is sweet, than it has sugar.

Aim: How do we solve logic problems using conditionals?

Conditional- asserting that the existence or occurrence of one thing or event depends on the existence or occurrence of another thing or event; hypothetical.
an example of a logical conditional in math would be: If there is a fire, than there would be smoke.


If you want to solve problems such as what is the contrapositive of this statement you would have to change certain parts of the sentence.
Contrapositive- the inference drawn from a statement and negating the terms and changing the order.


The contrapositive of the conditional example would be: If there is no smoke, than there is no fire.


Find the contrapositive of this statement: If the television is on than electricity is being used.