Question

type the answer in the box. surface area

Explanation:

Step1: Identify the shape (square pyramid)

The figure is a square pyramid with a square base (side \( s = 16 \, \text{cm} \)) and triangular faces (slant height \( l = 17 \, \text{cm} \)).

Step2: Recall surface area formula for square pyramid

Surface Area (\( SA \)) of a square pyramid is \( SA = \text{Base Area} + \text{Lateral Surface Area} \).
Base Area (\( A_{\text{base}} \)): \( s^2 \) (since base is square).
Lateral Surface Area (\( A_{\text{lateral}} \)): \( 4 \times \frac{1}{2} \times s \times l = 2sl \) (4 triangular faces).

Step3: Calculate Base Area

\( A_{\text{base}} = 16^2 = 256 \, \text{cm}^2 \).

Step4: Calculate Lateral Surface Area

\( A_{\text{lateral}} = 2 \times 16 \times 17 = 544 \, \text{cm}^2 \).

Step5: Total Surface Area

\( SA = 256 + 544 = 800 \, \text{cm}^2 \).

Answer:

\( 800 \, \text{cm}^2 \)