1. The problem asks to explain the concept of slant height in a right square pyramid. 2. A right square pyramid has a square base and an apex directly above the center of the base, forming perpendicular height $h$. 3. The slant height $s$ is the length of the line segment from the apex to the midpoint of any side of the square base along the triangular face. 4. To find $s$, consider the right triangle formed by: - the pyramid height $h$ - half the base side length $\frac{b}{2}$ - the slant height $s$ as the hypotenuse 5. Using the Pythagorean theorem: $$s^2 = h^2 + \left(\frac{b}{2}\right)^2$$ $$\Rightarrow s = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}$$ 6. For example, if $h=15$ cm and $b=10$ cm: $$s = \sqrt{15^2 + 5^2} = \sqrt{225 + 25} = \sqrt{250} = 5\sqrt{10}$$ cm 7. The slant height $s$ serves as the height of each triangular face of the pyramid. 8. This height is essential for calculating the area of one triangular face: $$\text{Area} = \frac{1}{2} \times b \times s$$ 9. Finally, knowing all triangular face areas plus base area allows calculation of total surface area. This explanation details the geometric meaning and calculation of slant height.