Question

find the lateral surface area of this square-based pyramid.
10 ft
10 ft
lsa = ? ft²

Explanation:

Step1: Identify the shape of the lateral faces

A square - based pyramid has 4 triangular lateral faces. Each triangular face has a base of length \(b = 10\) ft and we assume the slant height (the height of each triangular face) is also \(l=10\) ft (from the diagram).

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). For one lateral triangular face, with \(base = 10\) ft and \(height=10\) ft, the area of one face is \(A_{1}=\frac{1}{2}\times10\times10 = 50\) \(ft^{2}\).

Step3: Calculate the lateral surface area (LSA)

Since there are 4 identical triangular lateral faces, the lateral surface area \(LSA=4\times A_{1}\). Substituting \(A_{1} = 50\) \(ft^{2}\), we get \(LSA=4\times50=200\) \(ft^{2}\).

Answer:

\(200\)