Finding the surface area of the square Pyramid
The surface area of a square pyramid can be found using the formula:
Surface area = base area + (0.5 × perimeter of base × slant height)
where the base is a square and the slant height is the distance from the apex (top of the pyramid) to the center of one of the square's sides.
Let's say the length of the square base is 8 cm, and the height of the pyramid (distance from the apex to the center of the base) is 10 cm.
1. Base area = 8 cm x 8 cm = 64 cm²
2. Perimeter of base = 4 x 8 cm = 32 cm
3. Slant height = √(10 cm)^2 + (4 cm)^2 (using Pythagorean theorem)
= √116
≈ 10.77 cm
Now we can plug these values into the formula:
Surface area = 64 cm² + (0.5 × 32 cm × 10.77 cm)
= 64 cm² + 172.16 cm²
= 236.16 cm²
Therefore, the surface area of the square pyramid is 236.16 cm².