To find the slant height of a square pyramid, you can use the following formula:
Slant Height (l) = √( (1/2 * base length)² + height² )
Here’s a step-by-step explanation:
- Identify the base length and height: The base length is the length of one side of the square base, and the height is the perpendicular distance from the base to the apex (top point) of the pyramid.
- Calculate half of the base length: Since the pyramid is square, you take half of the base length.
- Square the half base length: Multiply the half base length by itself to get (1/2 * base length)².
- Square the height: Do the same for the height, calculating height².
- Add the two squared values: Now, add the results from the previous two steps together.
- Take the square root: Finally, take the square root of the sum. The result will give you the slant height of the pyramid.
For example, if the base length of a square pyramid is 8 units and the height is 6 units, here’s how you’d calculate it:
- Half of the base length = 8 / 2 = 4 units
- Square of half base length = 4² = 16
- Square of height = 6² = 36
- Sum = 16 + 36 = 52
- Slant Height = √52 ≈ 7.21 units
So, the slant height of the pyramid in this example would be approximately 7.21 units.