Can you find x for the following equation? 7x+12=3(5x-12)
2 answers:
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Answers:
- a) 15.6
- b) 12
- c) 36
- d) 51.6
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Explanations:
Part (a)
The area of a triangle formula is A = 0.5*b*h where b and h are the base and height. You could use 1/2 in place of the 0.5
We're focused on the blue shaded triangle, which is the "floor" so to speak of this pyramid. To find the floor area, we will use b = 6 and h = 5.2 and we get
A = 0.5*b*h = 0.5*6*5.2 = 15.6
For this problem, all areas are in square inches as denoted by the
If you're curious where the b = 6 came from, it's because all sides of the equilateral triangle are the same length.
Note: The base and height of a triangle are always perpendicular.
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Part (b)
Focus on any single non-shaded triangle. Let's say we focus on the upper triangle. We have b = 6 and h = 4. It then leads to the area A = 12 sq in. This is the area of one lateral face.
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Part (c)
The instructions state that the lateral faces are congruent triangles, aka they are identical triangles. So that means we have three copies of the same area we found back in part (b), which was 12. Therefore, the lateral surface area is 3*12 = 36 square inches. As your teacher mentions, we do <u>not</u> include the shaded triangle as part of this result (that will happen in part d below).
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Part (d)
We add the results of parts (a) and (c) together to get the full surface area. This is the total area of the flat net, and it corresponds directly to the full surface area because we fold up the 2D figure to get the 3D one.
The total surface area is 15.6+36 = 51.6 in^2
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Side note: Another name for "triangular pyramid" is "tetrahedron". The "tetra" means "four", and "hedron" means "face".