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Question 18 : 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

1. 10\\sqrt{2})
2. 8\\sqrt{3})
3. 12
4. 5\\sqrt{5})

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Video Explanation

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Explanatory Answer

It is given that the diagram is a square pyramid and all 4 sides of the triangle are of equal sides.
Now, we need to plug in a right triangle and apply Pythagoras theorem to find the vertical height of the triangle.
Draw a vertical from the apex of the pyramid and draw a line to the base along the equilateral triangle. Connect the points in the base to form a right triangle.
The hypotenuse would be the slant height of the pyramid, which is the altitude of the equilateral triangle.
Length of the base = 10 cms
Hypotenuse = Altitude of the equilateral triangle = x 20 = 10cms
Therefore, (Vertical height)² = (10)² - 10² = 200
Vertical height = = 10cms

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The question is "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"

Hence, the answer is 10\\sqrt{2})

Choice A is the correct answer.