what is the surface area of a square pyramiid where the base eage is 2.5cm and the slant height is 5cm round your answer to the nearest hundredth keep in mind that you have the slant height responses 18.75cm 27.5cm 31.25cm 21.0cm
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of each triangular face.
The base of the square pyramid is a square, so its area can be calculated by squaring the length of one side (also known as the base edge). In this case, the base edge is 2.5 cm, so the area of the base is (2.5 cm)^2 = 6.25 cm^2.
The pyramid has 4 identical triangular faces, each with a base equal to the base edge and a height equal to the slant height. The area of each triangular face can be calculated using the formula:
Area = (1/2) * base * height
Substituting the values we have:
Area = (1/2) * 2.5 cm * 5 cm = 6.25 cm^2
Since the pyramid has 4 identical triangular faces, the total surface area (SA) is:
SA = area of the base + 4 * area of a triangular face
= 6.25 cm^2 + 4 * 6.25 cm^2
= 6.25 cm^2 + 25 cm^2
= 31.25 cm^2
Therefore, the surface area of the square pyramid is 31.25 cm^2.