what is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth.
_____ cm^2
The slant height of a pyramid is the distance from the apex (top) of the pyramid to any point on the base edge.
The formula to find the surface area of a square pyramid is given by:
Surface area = base area + (0.5 × perimeter of base × slant height)
In a square pyramid, the base area is equal to the area of a square, which is side length squared. In this case, the side length is 1.5 cm, so the base area is 1.5 cm * 1.5 cm = 2.25 cm^2.
The perimeter of a square is found by multiplying the length of one side by 4. So, the perimeter of the base in this case is 1.5 cm * 4 = 6 cm.
Now, we can calculate the surface area:
Surface area = 2.25 cm^2 + (0.5 × 6 cm × 4 cm)
Surface area = 2.25 cm^2 + (3 cm * 4 cm)
Surface area = 2.25 cm^2 + 12 cm^2
Surface area = 14.25 cm^2
To round it to the nearest hundredth, the surface area of the given square pyramid is approximately 14.25 cm^2.