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
To find the surface area of a square pyramid, we need to add together the areas of the four triangular faces (each with a base equal to the length of one side of the square base, and a height equal to the slant height), plus the area of the square base.
The area of a triangular face can be calculated using the formula (base × height) / 2.
Given that the base edge is 1.5 cm and the slant height is 4 cm, the height of each triangular face is 4 cm.
The area of each triangular face is then (1.5 cm × 4 cm) / 2 = 3 cm².
Since there are four triangular faces, the total area for all the triangular faces is 4 × 3 cm² = 12 cm².
The area of the square base is the length of one side squared, so 1.5 cm × 1.5 cm = 2.25 cm².
Therefore, the total surface area of the pyramid is 12 cm² + 2.25 cm² = 14.25 cm².
Rounded to the nearest hundredth, the surface area of the given square pyramid is 14.25 cm².