Question

follow the steps to find the surface area of the square pyramid.
what is the area of
all 4 triangles?
square base: 64 cm²
triangles ×4: ?
(image shows a square pyramid with base edges 8 cm and a slant height (blue line) of 14 cm, and a smaller pyramid diagram)

Explanation:

Step1: Find base of triangle

The base of each triangular face is equal to the side length of the square base. Since the area of the square base is \(64\space cm^2\), the side length \(s\) of the square is \(\sqrt{64} = 8\space cm\) (because area of square \(A = s^2\), so \(s=\sqrt{A}\)). So each triangle has a base \(b = 8\space cm\).

Step2: Find area of one triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). Here, the height of each triangular face (the slant height) is given as \(14\space cm\). So the area of one triangle is \(\frac{1}{2}\times8\times14\).
Calculating that: \(\frac{1}{2}\times8\times14 = 4\times14= 56\space cm^2\).

Step3: Find area of 4 triangles

Since there are 4 identical triangular faces, we multiply the area of one triangle by 4. So \(4\times56 = 224\space cm^2\).

Answer:

\(224\space cm^2\)