Slant Height 0D92Df

1. **Problem Statement:** Calculate the slant height of a pyramid to the nearest tenth. 2. **Understanding the Slant Height:** The slant height ($l$) of a pyramid is the distance from the apex (top point) of the pyramid down the face to the midpoint of a side of the base. 3. **Formula:** For a right pyramid with a regular polygon base, the slant height can be found using the Pythagorean theorem: $$l = \sqrt{h^2 + r^2}$$ where $h$ is the height of the pyramid (perpendicular from apex to base) and $r$ is the apothem (distance from center of base to midpoint of a side). 4. **Step-by-step Calculation:** - Identify the height $h$ of the pyramid. - Identify or calculate the apothem $r$ of the base. - Substitute values into the formula. 5. **Example:** Suppose the height $h = 12$ units and the apothem $r = 5$ units. $$l = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$$ 6. **Rounding:** The slant height is $13.0$ units to the nearest tenth. **Final answer:** The slant height of the pyramid is $13.0$ units.