Final answer:
To find the lateral surface area of a square pyramid, you need to find the area of each triangular face and add them together. Let's assume that the base side length of the square pyramid is 8cm. Using the Pythagorean theorem, we can find the slant height. Once we have the slant height, we can calculate the area of each triangular face and add them to find the total lateral surface area.
Step-by-step explanation:
To find the lateral surface area of a square pyramid, we need to find the area of each triangular face and add them together. The lateral surface area is equal to the sum of the areas of the four triangular faces.
Since the base of the square pyramid is a square, the height of each triangular face is the slant height, which can be found using the Pythagorean theorem.
Let's assume that the base side length of the square pyramid is 8 cm. We can find the slant height using the formula:
slant height (l) = √(height of triangular face)^2 + (base side length/2)^2
Plugging in the values, we get:
l = √(6^2 + (8/2)^2) = √(36 + 16) = √52 ≈ 7.211 cm
Now, we can find the area of each triangular face using the formula:
area of triangular face = (base side length * slant height) / 2
So, the area of each triangular face is:
Area = (8 * 7.211) / 2 = 28.844 cm²
Since there are four triangular faces, the total lateral surface area is:
Lateral Surface Area = 4 * 28.844 = 115.376 cm²