Question

find the surface area of a square pyramid with side length 2 cm and slant height 3 cm.

Explanation:

Step1: Calculate the base area

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

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). Here, the base of the triangle is the side - length of the square base (\(b = 2\) cm) and the height of the triangle is the slant height (\(l = 3\) cm).
\(A_{triangle}=\frac{1}{2}\times2\times3 = 3\) \(cm^{2}\)

Step3: Calculate the total area of the four triangular faces

Since there are 4 congruent triangular faces in a square pyramid, \(A_{triangles}=4\times A_{triangle}\)
\(A_{triangles}=4\times3=12\) \(cm^{2}\)

Step4: Calculate the total surface area

The total surface area of a square pyramid \(A = A_{base}+A_{triangles}\)
\(A=4 + 12=16\) \(cm^{2}\)

Answer:

\(16\) \(cm^{2}\)