How do I find the slant height of a figure?

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Finding the Slant Height of a Figure

The slant height is a crucial measurement, particularly in geometry when dealing with conical shapes, pyramids, or right triangular prisms. It represents the distance measured along the lateral surface from a point on the base to the apex (the top point) of the figure. Here’s how to find it, depending on the type of figure you are dealing with:

1. For a Cone:

To find the slant height (denoted as l) of a cone, you can use the Pythagorean theorem. The formula is:

l = √(r² + h²)

Where:

  • r = radius of the base of the cone
  • h = height of the cone (vertical height from the base to apex)

Thus, you first square the radius and height, sum those values, and then take the square root of the result to obtain the slant height.

2. For a Pyramid:

For a square pyramid, the slant height can be found by:

l = √(s² + (h/2)²)

Where:

  • s = length of one side of the base square
  • h = vertical height of the pyramid

In this case, you’ll divide the height by 2 to find the distance from the center of the base to the apex when creating a right triangle, and then apply the Pythagorean theorem.

3. General Steps to Follow:

  1. Gather required measurements: radius and height for a cone; side length and height for a pyramid.
  2. Plug the measurements into the applicable formula based on the shape of the figure.
  3. Perform calculations, ensuring to follow the order of operations.
  4. Double-check your calculations to ensure accuracy.

By following these steps, you should be able to find the slant height of the figure accurately. Happy calculating!

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