Question 1: What is the Pythagorean Theorem? You should use words, pictures, symbols and numerical examples. (10 Marks)
"A" stands for altitude, "B" stands for base, and "C" stands for hypotenuse.
In this diagram, we do not know the measurement of C. To find C, we use the Pythagorean Theorum. The Pythagorean Theorum is that the altitude of a right triangle squared added to the base of a right triangle squared is equal to the hypotenuse of a right triangle squared. We do this:
4.5 squared + 6 squared = C squared
20.25 + 36 = C squared
56.25 = C squared
Now, you have to find the square root of 56.25. Don't forget our algebra unit; what you do to one side you must do to the other.
The square root of C squared is C.
The square root of 56.25 is 7.5.
The hypotenuse in this diagram is 7.5 meters.
For this question, our altitude is missing. But we still use the Pythagorean Theoru. We do this :
A squared + 6 squared = 10 squared
A squared + 36 = 100
A squared = 100 - 36
A squared = 64
Now we have the same last step as our first question, and we do the same thing. Figure out the square roots:
The square root of A squared is A.
The square root of 64 is 8.
Therefore, the altitude of this right triangle is 8.
Question 2: How do you find the surface area of a right rectangular prism? You should use words, pictures, symbols and numerical examples.(10 Marks)
A right rectangular prism is a 6-sided rectangle with all right angles. To find out the surface area of a right rectangular prism, you must use this formula:
2(LH) + 2(LW) + 2(HW)
You use this formula because there are 6 sides, front, back, left, right, top, and bottom. The front and the back have the same height, lenght, and width, left and right have the same heigh, length, and width, and top and bottom have the same height, length, and width.
These are two pictures of rght rectangular prisms that i found on the internet:
Alright, to figure out the Surface Area of this net we will use this formula:
2(LH) + 2(LW) + 2(HW)
So, our problem should look like this:
2(5x5) + 2(5x3) + 2(5x3)
Now, we multiply:
2(25) + 2(15) + 2(15)
Again, we multiply:
50 + 30 + 30
Now all we have to do is add:
110
Our Surface Area is 110 meters.
Question 3: How do you find the surface area of a right cylinder? You should use words, pictures, symbols and numerical examples. (10 Mark)
To find the surface area of a right cylinder, you must use this formula:
2(3.14 or pi) r squared + 2 (3.14 or pi) r h
(r stands for the radius, h stands for height)
The radius for this cylinder is 3 cm, the height 9 cm. Can you figure out how to do it?
Well it doesnt matter if you can or not, cause i'm going to tell you anyway:)
We do this:
2(3.14) 3 squared + 2 ( 3.14) (3) (9)
2 (3.14) 9 + 2 (3.14) (3) (9)
6.28 (9) + 6.28 (3) (9)
56.25 + 18.84 (9)
56.25 + 169.56
SA = 225.81 cm squared
What is a polygon and how do we classify one? (10 Marks)
A regular polygon is a polygon whose sides are all the same and whose angles are all equal , whereas an irregular poygons sides are different in length and the angles are different measurements. To classify a polygon, you first need to know the exact definition of a polygon.Definition : any closed figure with 3 or more straight sides.The next step to classifying a polygon, would be to determine whether it is a regular or irregulat polygon, using the definitons above it shouldnt be too difficult. And then, your done classifying ! :)
This picture below is an example of some classified polygons :
SA= 2 pi r
In a right triangle, the longest side is always that diagonal one called the hypotenuse (C). The hypotenuse is always the side on the opposite of the right angle, which is where the altitude (A) and the base (B) meet.
