Question

The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h? Round your answer to the nearest tenth.

a) 6.3 units
b) 6.7 units
c) 7.2 units
d) 7.5 units

Answer 1

To find the vertical height of a square pyramid, use the Pythagorean Theorem with the slant height and half the length of the base. The vertical height is approximately 6.2 units. The correct answer is option (a)

Step-by-step explanation:

To find the vertical height of the square pyramid, we can use the Pythagorean Theorem. The slant height of the pyramid is the hypotenuse of a right triangle formed by the height, the slant height, and half the length of the base. We know that the slant height is 8 units and half the length of the base is 5 units. Let's call the height h. Using the Pythagorean Theorem, we have h^2 + 5^2 = 8^2. Solving for h, we get h^2 + 25 = 64. Subtracting 25 from both sides, we have h^2 = 39. Taking the square root of both sides, we have h = √39. Calculating this value, the vertical height of the pyramid is approximately 6.2 units. Therefore, the correct option is a) 6.3 units.