Find the surface area of the a square pyramid.The A = 3 m and H = 4.5 m?
To find the surface area of a square pyramid, you need to calculate the area of each of its faces and then sum them up.
1. Base Area:
Since the base of the pyramid is a square, you can use the formula for the area of a square, which is side length squared (A = s^2).
Given that A = 3 meters, you can find the side length of the base square by taking the square root of A.
s = √A = √3 = 1.73 meters
The area of the base (B) is then calculated as B = s^2 = (1.73)^2 = 3 meters squared.
2. Triangle Faces:
In a square pyramid, there are four triangular faces. The area of each triangular face can be calculated using the formula: A = 0.5 * base * height.
The height (H) of the pyramid is given as 4.5 meters, and the base length (s) of the triangle is the same as the side length of the base square, which we previously found as 1.73 meters.
Hence, the area of each triangular face is A = 0.5 * base * height = 0.5 * 1.73 * 4.5 = 3.88 meters squared.
Since there are four triangular faces, the total area of the triangular faces is 4 * 3.88 = 15.52 meters squared.
3. Add the areas:
To calculate the total surface area (SA) of the square pyramid, you sum up the area of the base and the area of the triangular faces.
SA = B + total triangular face area = 3 + 15.52 = 18.52 meters squared.
Therefore, the surface area of the square pyramid is 18.52 meters squared.