What is the surface area of a square pyramid where the base edge is 1.5 and the slant height is 4 round your answer to the nearest hundredth
To find the surface area of a square pyramid, we need to find the area of the base and the areas of the four triangular faces.
First, let's calculate the area of the base. Since it is a square, the formula to find the area is side length squared. In this case, the side length is 1.5, so the area of the base is 1.5^2 = 2.25.
Next, let's calculate the area of each triangular face. In a square pyramid, all four triangular faces have the same dimensions.
We know the slant height is 4, which is the height of the triangles. The base of each triangle is the same as the base edge of the pyramid, which is 1.5.
The formula for the area of a triangle is 1/2 * base * height.
Using this formula, we can calculate the area of each triangular face: 1/2 * 1.5 * 4 = 3.
Since there are four triangular faces, the total area of the triangular faces is 4 * 3 = 12.
Finally, we can find the surface area of the square pyramid by summing up the area of the base and the area of the triangular faces: 2.25 + 12 = 14.25.
Therefore, the surface area of the square pyramid is approximately 14.25, rounded to the nearest hundredth.