Question

what is the surface area of the square pyramid? 3 2 square units

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 2\). The area of a square is \(A_{base}=a^{2}\), so \(A_{base}=2^{2}=4\).

Step2: Calculate the area of one triangular face

The base of each triangular face is \(b = 2\) and the height (slant height) is \(h = 3\). The area of a triangle is \(A_{triangle}=\frac{1}{2}\times b\times h\). Substituting the values, we get \(A_{triangle}=\frac{1}{2}\times2\times3 = 3\).

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=4\times A_{triangle}\). So \(A_{triangles}=4\times3=12\).

Step4: Calculate the total surface area

The total surface area \(A\) of the square - pyramid is the sum of the area of the base and the area of the triangular faces. \(A=A_{base}+A_{triangles}\). Substituting the values, we get \(A = 4+12\).

Answer:

\(16\)