Answers:
- a) 693 sq cm (approximate)
- b) 48 sq cm (exact)
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Explanation:
Part (a)
A regular triangular pyramid, aka regular tetrahedron, has all four triangles that are identical copies of one another. They are congruent triangles. This will apply to part (b) as well.
To find the area of one of the triangles, we'll use the formula
A = 0.25*sqrt(3)*x^2
where x is the side length. This formula applies to equilateral triangles only.
In this case, x = 20, so
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*20^2
A = 173.20508 approximately
That's the area of one triangle, but there are four total, so the entire area is about 4*173.20508 = 692.82032 which rounds to 693 sq cm.
The units "sq cm" can be written as "cm^2".
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Part (b)
We'll use the same idea as part (a). But the formula to find the area of one triangle is much simpler.
The area of one of the triangles is A = 0.5*base*height = 0.5*6*4 = 12 sq cm.
So the area of all four triangles combined is 4*12 = 48 sq cm
This area is exact.
The area of each 2D flat net corresponds exactly to the surface area of each 3D pyramid. This is because we can cut the figure out and fold along the lines to form the 3D shapes.
Answer: The average age is 7.1 years.
This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.
To start, lets multiply the total number of children by their individual ages.
6 x 5 = 30 years
14 x 8 = 112 years
There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.
Answer:
I think A
Step-by-step explanation:
Can you mark me brainliest because I am almost to level ace!
Judging on the question I figured that the perpendicular line's slope would be -x since the slope of a perpendicular line is opposite to that of a the reference line.
Thus, your answer should be y=-x+4 considering that is the only equation with the slope of -x.
13 3/4 + x = 7 1/4
becomes x = 13 3/4 / 7 1/4
13 3/4 = 55/4
7 1/4 = 29/4
55/4 / 29/4 = 55/4 * 4/29 = 220/116
220/116 reduces to 1 26/29
