Question 7(Multiple Choice Worth 2 points)
(Types of Area MC)
A pyramid has a square base with side lengths of 9 centimeters. The slant height of the faces is 12 centimeters. What is the surface area of the pyramid?
$216 \mathrm{~cm}^{2}$
$252 \mathrm{~cm}^{2}$
$297 \mathrm{~cm}^{2}$
$513 \mathrm{~cm}^{2}$

Step 1 ：The surface area of a pyramid is given by the formula: \(\text{Surface Area} = \text{Base Area} + \frac{1}{2} \times \text{Perimeter of Base} \times \text{Slant Height}\)

Step 2 ：Here, the base is a square with side length 9 cm, so the base area is \(9 \times 9 = 81 \, \text{cm}^2\).

Step 3 ：The perimeter of the base is \(4 \times 9 = 36 \, \text{cm}\).

Step 4 ：The slant height is given as 12 cm.

Step 5 ：Substituting these values into the formula, we get: \(\text{Surface Area} = 81 \, \text{cm}^2 + \frac{1}{2} \times 36 \, \text{cm} \times 12 \, \text{cm} = 81 \, \text{cm}^2 + 216 \, \text{cm}^2 = 297 \, \text{cm}^2\).

Step 6 ：\(\boxed{\text{So, the surface area of the pyramid is 297 cm}^2}\)