Question

A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.8 in. The slant height of the pyramid is 90.1 in. What is the height of the pyramid?

Answer 1

The height of the heater is about 89.3 in.

You can solve this problem with the Pythagorean Theorem. The base is a square. So half way across the middle will the right under the tip of the pyramid. We can use the measurement with the slant height to write and solve the equation below.

23.8^2 + x^2 = 90.1^2
x will be about 89.3.

Answer 2

Answer:

Height of the pyramid is 86.9 in

Step-by-step explanation:

The length of the pyramid, the height and the slant height forms a triangle.

Given that

L = The length of one side of the base = 23.8 in.

S = The slant height of the pyramid = 90.1 in.

The height of the pyramid is calculated as follows.

Let H = height of pyramid.

Using Pythagoras theorem

S² = H² + L²

Substitute values

90.1² = H² + 23.8² --- collect like terms

H² = 90.1² - 23.8²

H² = 8118.01 - 566.44

H² = 7551.57 --- Take Squareroot of both sides

√H² = √7551.57

H = √7551.57

H = 86.899 in

H = 86.9 in --- Approximately.

Hence, the Height of the pyramid is 86.9 in