### Square Pyramid Calculation #### Problem Description You are given a square pyramid with the following dimensions: - Base length (\(b\)) = 6 inches - Slant height (\(s\)) = 12 inches The goal is to solve for the surface area and volume of the square pyramid. #### Diagram Explanation The provided diagram is a 3D representation of a square pyramid: - The base (\(b\)) is a square with highlighted edges. - The slant height (\(s\)) is the length from the top vertex perpendicular to the midpoint of an edge of the square base. - The pyramid's height (\(h\)) is not explicitly given but can be calculated if needed. #### Steps to Solve 1. **Surface Area Calculation:** The formula for the surface area (\(SA\)) of a square pyramid is: \[ SA = b^2 + 2b \cdot s \] where: - \(b^2\) is the area of the square base. - \(2b \cdot s\) is the combined area of the four triangular faces. 2. **Volume Calculation:** The formula for the volume (\(V\)) of a square pyramid is: \[ V = \frac{1}{3} b^2 \cdot h \] To find \(h\) (the height of the pyramid), use the Pythagorean Theorem in the right triangle formed by the height (\(h\)), half of the base length (\(\frac{b}{2}\)), and the slant height (\(s\)): \[ s^2 = h^2 + \left(\frac{b}{2}\right)^2 \] To solve for \(h\): \[ h = \sqrt{s^2 - \left(\frac{b}{2}\right)^2} \] Once you have the values, you can plug them into their respective formulas to find the surface area and volume. #### Input Fields: - **Surface Area**: - A text box where the calculated surface area will be entered (in square inches). - **Volume**: - A text box where the calculated volume will be entered (in cubic inches). #### Help Options: - **Question Help**: - Video: A video