The surface area of a square pyrami is 480 sq . ft . If the length of the base 12 ft .. what is its slant height?

To find the **slant height** of the square pyramid, let's break down the given information and apply the relevant formulas. ### Given: - **Total Surface Area (S)** = 480 square feet - **Base Edge Length (b)** = 12 feet ### Components of Surface Area: 1. **Base Area (A₁):** Since the base is a square, \[ A₁ = b^2 = 12^2 = 144 \text{ sq. ft} \] 2. **Lateral Surface Area (A₂):** This comprises four triangular faces. The area of one triangular face is: \[ \text{Area of one triangle} = \frac{1}{2} \times b \times \text{slant height (s)} \] Therefore, for four triangles: \[ A₂ = 4 \times \left(\frac{1}{2} \times 12 \times s\right) = 2 \times 12 \times s = 24s \] ### Total Surface Area: \[ S = A₁ + A₂ = 144 + 24s = 480 \] ### Solving for Slant Height (s): \[ 144 + 24s = 480 \\ 24s = 480 - 144 \\ 24s = 336 \\ s = \frac{336}{24} \\ s = 14 \text{ feet} \] ### **Answer:** The slant height of the pyramid is **14 feet**.