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
The surface area of a square pyramid can be calculated by finding the area of the base and adding the areas of the four triangular faces.
The area of the base can be found by squaring the length of one edge:
Area of base = (1.5 cm)^2 = 2.25 cm^2
The area of each triangular face can be found by using the formula for the area of a triangle:
Area of triangular face = (1/2) * base * height
Since the triangular faces in a square pyramid are all congruent, we only need to calculate the area of one of them.
The base of the triangle is the length of one edge of the square base, which is 1.5 cm.
The height of the triangle can be found using the Pythagorean theorem, since the height, slant height, and half of the base form a right triangle.
Height^2 + (1.5/2)^2 = 4^2
Height^2 + 0.75^2 = 16
Height^2 = 16 - 0.5625 = 15.4375
Height ≈ √15.4375 ≈ 3.93 cm
Plugging in the values into the formula:
Area of triangular face = (1/2) * 1.5 cm * 3.93 cm ≈ 2.945 cm^2
Now, we can calculate the surface area by adding the areas of the base and the four triangular faces:
Surface area = (2.25 cm^2) + (4 * 2.945 cm^2) ≈ 15.08 cm^2
So, the surface area of the square pyramid is approximately 15.08 cm^2.