Question

1. determine the surface area of the square pyramid shown below. express your answer in square centimeters

28 mm
38 mm

Explanation:

Step1: Calculate base area

The base is a square with side length 28 mm. Area of square:
$\text{Base Area} = 28^2 = 784$ mm²

Step2: Calculate one triangular face area

Each triangular face has base 28 mm, slant height 38 mm. Area of triangle:
$\text{One Face Area} = \frac{1}{2} \times 28 \times 38 = 532$ mm²

Step3: Calculate total lateral face area

There are 4 identical triangular faces:
$\text{Total Lateral Area} = 4 \times 532 = 2128$ mm²

Step4: Calculate total surface area

Add base area and lateral area:
$\text{Total Surface Area} = 784 + 2128 = 2912$ mm²

Step5: Convert to square centimeters

Since $1$ cm² = $100$ mm²:
$\text{Surface Area (cm}^2\text{)} = \frac{2912}{100} = 29.12$ cm²

Answer:

29.12 square centimeters