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.
What is the surface area of square pyramid with base length of 10cm and slant height of 20cm
1 answer