Question

Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.

Answer 1

the height of the square- based pyramid is 147. 06 feet long

How to determine the value

From the information given, we can deduce that the following;

• Height of the square pyramid is unknown
• sides are 34 feet long
• Edges are 50 feet long

Area of a triangle = 1/ 2 × base × height

Let's substitute the values of the parameters, we have

50² = 1/ 2 × 34 × height

Find the square and division

2500 = 17 × height

Make 'height' the subject of formula

Height = 2500/ 17

Height = 147. 06 feet long

Thus, the height of the square- based pyramid is 147. 06 feet long

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Answer 2

Answer:

  31√2 feet

Step-by-step explanation:

The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.

Setup

Let h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...

  h² +(17√2)² = 50²

Solution

Subtracting the constant on the left gives ...

  h² = 2500 -578 = 1992

  h = √1992 = 31√2

The height of the square pyramid is exactly 31√2 feet.

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Read more about the Pythagorean theorem here:

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