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 awnser to he nearest hunderedth
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base is simply the length of one side squared: (1.5 cm)^2 = 2.25 cm^2.
To find the area of each triangular face, we can use the formula: Area = 1/2 * base * height.
The base of each triangular face is equal to the length of one side of the square base (1.5 cm). The height can be found using the Pythagorean theorem, where the slant height (4 cm) is the hypotenuse and the height is one of the legs:
height = √(slant height^2 - base^2) = √(4 cm^2 - 1.5 cm^2) ≈ √(14.75 cm^2) ≈ 3.84 cm.
Now, we can calculate the area of each triangular face:
Area = 1/2 * base * height = 1/2 * 1.5 cm * 3.84 cm ≈ 2.88 cm^2.
Since there are four triangular faces, the total surface area is:
Surface area = base area + 4 * triangular face area = 2.25 cm^2 + 4 * 2.88 cm^2 = 2.25 cm^2 + 11.52 cm^2 ≈ 13.77 cm^2.
Rounded to the nearest hundredth, the surface area of the square pyramid is approximately 13.77 cm^2.