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Math Grade 8 Unit Three: How to calculate surface area, volume and building and sketching objects
Transcript of Math Grade 8 Unit Three: How to calculate surface area, volume and building and sketching objects
area Lesson three: How to calculate the volume Conclusion This procedural text will teach you how to calculate the surface area, volume and building and sketching objects. This unit in math is originally very easy to understand once explained properly and found closer to grade 7 level than grade 8. There are many possible ways to calculate surface areas and volumes, choose the best method for you! This triangular prism is a 3 dimensional figure. The key to calculate the surface area of a triangular prism is to understand the formula base x height ÷ two. Base times height is very similar to length x width of a rectangular prism but since all the angles to a rectangular prism add up to be 360° and triangular prism angles are only 180°, after multiplying base x height, you MUST divide it by two.
Note: 180° is the half of 360°, this is why after calculating base x height for a triangle, it is divided in two. Another way to calculate the surface area is using the simple addiction and multiplication way. This formula to calculate the surface area takes longer than the formula shown before. () Here is a legend for math on what each letter means before you get started: You have already learned the surface area formula and how to calculate them. You have also learned how to draw figured with different views. This is now the last lesson of unit 5, which is how to calculate the volume of a triangular prism! This unit is fairly easy depending on whether you know previous formulas given to you in grade 6 and 7. After you have all the formulas memorized, the next step is only to verify your work! If you follow and understand all these lessons, you will be sure to ace your tests in this unit! Though, the top, front and side views of the triangular prism below are 2 dimensional figures. These 2 dimensional figures or more considered as views, add up to one 3 dimensional triangular prism. Why do I need to learn views of the object when I can already draw the 3 dimensional object? To use another method of looking at views, you may benefit the usage of linking cubes to see all the views in front of your own eyes. The image below are linking tubes. You can buy these everywhere (walmart, costco). After you observe the views of the figure, draw the views on a piece of grid paper. Questions
1. Make a figure with linking cubes. Then, draw the views
2. Draw the views of this given figure below. The formula to calculate a triangle: base x height
SA= Surface area
b= Base of triangle
h= Height of triangle Example: Find the base and height of the prism below. To find the base and height of the triangular prism, and not the length of the triangular prism, you find the face that is a triangle and not a rectangle or square. After the base and height are found, choose a base and a height (bases to heights must always have a 90° angle) In this formula, you must calculate area of the sides of the three rectangles. Rectangle a, b and c. To calculate an area, it is length * width. Which, in this case, is a*l, b*l and c*l. a, b and c replace the widths which is why widths are not multiplied with lengths.
In symbols, the formula of the surface area is : a×l+b×l+c×l × 2 × b × h ÷ 2 or SA=al+bl+cl+bh
Note: b is widh and base of the triangle too. It is the only rectangle connected to the triangles. In the example above, the height of both triangles are 5cm, rectangle A has a length of 5cm, rectangle B has a length of 6cm and rectangle C has a length of 7 cm. The widths for all triangles is 3cm.
So, 3×5(area of A) + 3×6 (area of B)+ 3×7(area of C) × 2 × b×h ÷ 2 l=Length of a rectangle
a and c=triangular prism rectangle's width
b= base of triangle (which means a width of a triangle)
h=height of a triangle
Remember: length and widths can NEVER be in a triangle. The mathematical term for length and widths in a triangle are base and height. This is a base and a height for a triangle (b=base h=height). (Note: the height does not necessarily always have to be on the side of a triangle, it is measured from the base until the highest vertex of the triangle.) The views are two dimensional drawings to give more information about the shape of the object. If you move on to drawing harder figures later on, you need to verify and determine all the views before turning that figure in to 3D. Note: the volume of any prism is the area of its
base × length of the prism. Critical question:
If the formula to calculate the volume for any prism is true, how can you find the formula to calculate the volume of a triangular prism? Answer: If a triangle is half a rectangle or square (triangle=180° rectangle=360°), then the area of the base for a triangle is b×h÷2. We divide the fraction of base and height by 2 because a triangle is half of a quad polygon (polygon with 4 sides). Therefore, the formula to find the volume of a triangular prism is
b=base of triangle
h=height of triangle
l=length (in this case it is the length of the prism)