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The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is
(2019)
- a)10√2
- b)5√5
- c)8√3
- d)12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The base of a regular pyramid is a square and each of the other four s...
From the diagram, it is clear that AB is the slant height of the equilateral triangle and is also the slant height of the pyramid.
On applying Pythagoras theorem in triangle AOB,
OB2 = AB2 – OA2 = (10√3 )2 − 102 = 200
∴ Height of the pyramid OB = 10√2 cm
Most Upvoted Answer
The base of a regular pyramid is a square and each of the other four s...
To find the vertical height of the pyramid, we need to find the height of one of the equilateral triangles that make up the sides of the pyramid.
The height of an equilateral triangle can be found using the formula:
height = (sqrt(3)/2) * side length
In this case, the side length of the equilateral triangle is 20 cm, so the height of one triangle is:
height = (sqrt(3)/2) * 20
height = 10sqrt(3) cm
Since there are four triangles, the total height of the pyramid is:
total height = 4 * height
total height = 4 * 10sqrt(3) cm
total height = 40sqrt(3) cm
Therefore, the vertical height of the pyramid is 40sqrt(3) cm.
So the answer is (2019) b) 40sqrt(3)
The height of an equilateral triangle can be found using the formula:
height = (sqrt(3)/2) * side length
In this case, the side length of the equilateral triangle is 20 cm, so the height of one triangle is:
height = (sqrt(3)/2) * 20
height = 10sqrt(3) cm
Since there are four triangles, the total height of the pyramid is:
total height = 4 * height
total height = 4 * 10sqrt(3) cm
total height = 40sqrt(3) cm
Therefore, the vertical height of the pyramid is 40sqrt(3) cm.
So the answer is (2019) b) 40sqrt(3)
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The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is(2019)a)10√2b)5√5c)8√3d)12Correct answer is option 'A'. Can you explain this answer?
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