1. **Problem Statement:** Calculate the area of the square base of a pyramid with side length 6 inches. 2. **Formula:** The area of a square is given by $$A = s^2$$ where $s$ is the side length. 3. **Calculation:** Given $s = 6$ inches, $$A = 6^2 = 36$$ square inches. --- 1. **Problem Statement:** Calculate the slant height of a pyramid with side length $5\sqrt{3}$ cm, base length 10 cm, and height 11.2 cm. 2. **Formula:** Use the Pythagorean theorem for the slant height $l$: $$l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}$$ where $h$ is the height and $b$ is the base length. 3. **Calculation:** Given $h = 11.2$ cm, $b = 10$ cm, $$l = \sqrt{11.2^2 + \left(\frac{10}{2}\right)^2} = \sqrt{125.44 + 25} = \sqrt{150.44} \approx 12.27\text{ cm}$$ --- 1. **Problem Statement:** Calculate the surface area $S$ of a pyramid with base edges 48 inches, base length 6 feet, and slant height $\sqrt{21}$ feet. 2. **Convert units:** 6 feet = 72 inches, $\sqrt{21}$ feet = $\sqrt{21} \times 12$ inches. 3. **Formula:** Surface area of a square pyramid: $$S = b^2 + 2bl$$ where $b$ is base length and $l$ is slant height. 4. **Calculation:** Base area: $$b^2 = 48^2 = 2304\text{ in}^2$$ Slant height in inches: $$l = \sqrt{21} \times 12 \approx 4.58 \times 12 = 54.96\text{ in}$$ Lateral area: $$2bl = 2 \times 48 \times 54.96 = 5276.16\text{ in}^2$$ Total surface area: $$S = 2304 + 5276.16 = 7580.16\text{ in}^2$$ --- 1. **Problem Statement:** Calculate the surface area $S$ of a square pyramid with all edges 14 yards. 2. **Formula:** For a square pyramid with base side $s$ and slant height $l$: $$S = s^2 + 2sl$$ 3. **Given:** All edges are 14 yd, so base side $s = 14$ yd. 4. **Find slant height $l$:** Since all edges are equal, the pyramid is regular and slant height equals the edge length: $$l = 14\text{ yd}$$ 5. **Calculate surface area:** $$S = 14^2 + 2 \times 14 \times 14 = 196 + 392 = 588\text{ yd}^2$$