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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

- 10\\sqrt{2})
- 8\\sqrt{3})
- 12
- 5\\sqrt{5})

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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} - 10^{2 }= 200

Vertical height = = 10cms

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" **

**Choice A** is the correct answer.

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