Question: How do we find the surface area and lateral area of prisms and cylinders?

Answer: So first of all what are prisms and cylinders?
Well prisms are solids with bases that are two congruent polygons. And a cylinder is a solid with two congruent circular bases connected by a tube.

So how do you find the lateral area?
To find the lateral area of a prism you multiply the perimeter by the height. Formula--> L.A.=Ph
This formula represents P as the perimeter of one of the bases and h as the height.

To find the lateral area of a prism you multiply the radius of one of the bases times two then multiply it by the height and finally multiply it by π. Formula--> L.A.=2πrh 


And how do you find the volume?
To find the volume of a prism you multiply the base times the height. Formula--> V=Bh
This formula represents B as the base area and h as the height.

To find the volume of  a cylinder you multiply the radius by itself  and then times it by the height and finally multiply it by π.




NOW YOU TRY! :D
What is the area of the following prism?

Question: How do we identify solids?

Answer: A solid, which is also known as a 3D object because it has three dimensions: width, depth, and height.
Solids have two properties that make them solids: they have surface area and volume.
Volume is the space inside an object, and surface area is the outer measurement of the object.

Okay, so now let me tell you that there are two different types of solids: Polyhedra and Non-Polyhedra.

The rule for Polyhedra solids is that all the sides must be flat surfaces.
Examples of these types of solids are shown below:

The rule for Non-Polyhedra is the opposite, if one or more of the sides is curved then it is a non-polyhedra.
Examples of these types of solids are shown below:

NOW YOU TRY! :D

What type of solid is the shape below?

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

Answer: That's very easy, the area of a circle is given by the formula A= πr2(squared) where A is the area and r is the radius. 

P.s. sometimes the radius isn't given to you, instead you are given the diameter. But dont worry because the diameter is just the radius times 2. So all you need to do to find the radius is divide the diameter by two! :)


NOW YOU TRY! :D


Find the area of the circle:

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

Answer: Well you can divide a regular polygon into congruent isosceles triangles by drawing segments to each vertex, as shown in the following figure:

Regular Polygon Area Conjecture
The area of a regular polygon is given by the formulas: A=nas and A=Pa
                                                             2              2
Where A is the area, P is the Perimeter, a is the apothem, s is the length of sides, and n is the number of sides.
The apothem is the perpendicular bisector from the center of the polygon to the side.

As seen in the image above, to find the area all you have to do is follow either one of the formulas, right now i am going to use the formula: A=nas
                                                   2
So i will have to multiply 7(n) times 7(a) times 10(s) and divide it by 2. Thus, the area of the heptagon will be 245 square cm.


NOW YOU TRY! :D


Find the area of the following polygon:

Question: How do we find the area of parallelograms, kites, and trapezoids.

Answer: Woah that's a lot of shapes! :O
So lets start of with parallelograms :) and lets review what area is, area is the space inside a shape.

Okay so now, to find the area of a parallelogram you must multiply the base times the height. Its very similar to finding the area of a rectangle :) AREA=B*H

Okay lets move on into trapezoids:
To find the area of a trapezoid, you must add the two bases and divide them by two, then you multiply it by the height. It sounds a bit confusing so lets look at it visually :)

Finally. lets learn how to find the area of a kite:
To find the area of a kite you must multiply the two diagonals and divide them by two.

NOW YOU TRY! :D


Find the area of the following figure:

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

Answer: First of all what is area?
The area of a figure is the measure region enclosed by the figure.

Okay now that we know what area is, lets find out how to find the area of a rectangle! :D
The area of a rectangle can be found by multiplying the length(L) times the width(W). AREA=L*W

Figure 1

The area is measured in "units squared." If your rectangle is 5 inches long and 3 inches wide, to find the area you must multiply these two. so it would be: 5inches * 3 inches = 15inches(squared). Illustrated in Figure 1.

 Now lets find out how to find the area of a triangle. To find the area of a triangle you do one half the base times the height. AREA=(1/2)B*H

NOW YOU TRY! :D

Find the area of the rectangle above.

Question: How do we solve logic problems using conditionals?

Answer: I have already stated what a math statement is, but if you don't remember then i shall refresh your memory :)
A mathematical statement is a statement that can be judged to be true or false.
Ok now that we have gone over math statements, lets go over conditional.

A conditional falls under the category of logic in geometry. a conditional is a compound sentence created by putting together two sentences using the words "IF" and "THEN." A conditional is also made up of a hypothesis and a conlusion.

Example:
If I am laughing
then I am having fun
-The hypothesis of this conditional is "i am laughing" and the conclusion is "i am having fun."

NOW YOU TRY! :D


Form a conditional out of the following hypothesis and conclusion:
Hypothesis- it is raining
Conclusion- i will take my umbrella