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.(1 point)
cm2
To find the surface area of a square pyramid, you need to find the sum of the areas of all the faces.
The base of the square pyramid is a square, so the area of the base is equal to the length of one side squared. In this case, the base edge is 1.5 cm, so the area of the base is 1.5 cm * 1.5 cm = 2.25 cm².
The slant height is the height of the triangular faces of the pyramid. The slant height is given as 4 cm.
The triangular faces are isosceles triangles, so the area of each face can be calculated using the formula: (1/2) * base * height.
The height of the triangular face can be found using the Pythagorean theorem: height = √(slant height^2 - (base/2)^2) = √(4 cm^2 - (1.5 cm/2)^2) = √(4 cm^2 - 0.5625 cm^2) = √3.4375 cm^2 = 1.85 cm (rounded to the nearest hundredth).
The area of each triangular face is (1/2) * base * height = (1/2) * 1.5 cm * 1.85 cm = 1.3875 cm².
Since there are 4 triangular faces, the total surface area of the square pyramid is 4 * 1.3875 cm² = 5.55 cm² (rounded to the nearest hundredth).
Therefore, the surface area of the square pyramid is 5.55 cm².