What is the surface area of square pyramid with base length of 10cm and slant height of 20cm
To find the surface area of a square pyramid, we need to find the area of each face and add them together.
The square base of the pyramid has a side length of 10 cm, so its area is 10 cm * 10 cm = 100 square cm (1 face).
The slant height of the pyramid is 20 cm, and the height is a right triangle formed with the slant height and half the base side length (10 cm/2 = 5 cm). Using the Pythagorean theorem, we can calculate the height:
height^2 + (10 cm/2)^2 = 20 cm^2
height^2 + 25 cm^2 = 400 cm^2
height^2 = 400 cm^2 - 25 cm^2
height^2 = 375 cm^2
height ≈ √375 ≈ 19.37 cm
Now we can calculate the area of the triangular faces (4 faces). Each triangular face has a base equal to the side length of the square base (10 cm) and a height equal to the height we just found (19.37 cm):
Area of each triangular face = (1/2) * base * height = (1/2) * 10 cm * 19.37 cm = 96.85 square cm
Finally, we can calculate the total surface area by adding the areas of all the faces:
Total surface area = area of square base + 4 * area of triangular faces
Total surface area = 100 square cm + 4 * 96.85 square cm
Total surface area ≈ 100 square cm + 387.4 square cm
Total surface area ≈ 487.4 square cm
Therefore, the surface area of the square pyramid is approximately 487.4 square cm.