Question

find the lateral surface area of the following square - based pyramid: lsa = ? cm²

Explanation:

Step1: Find the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of each triangular face of the square - based pyramid is \(b = 6\space cm\) and the height (slant height) \(h=4\space cm\). So, the area of one triangular face \(A_{1}=\frac{1}{2}\times6\times4\).

$$A_{1}=\frac{1}{2}\times6\times4 = 12\space cm^{2}$$

Step2: Calculate the lateral surface area

A square - based pyramid has 4 triangular faces. The lateral surface area \(LSA\) is the sum of the areas of these 4 triangular faces. Since all 4 triangular faces are congruent (because it is a square - based pyramid), \(LSA = 4\times A_{1}\).
Substitute \(A_{1}=12\space cm^{2}\) into the formula: \(LSA=4\times12\)

$$LSA = 48\space cm^{2}$$

Answer:

\(48\)