Question

find the lateral surface area of this square-based pyramid. image of square - based pyramid with 10 ft labeled on base edge and 10 ft labeled on a slant - related edge lsa = ? ft²

Explanation:

Step1: Recall the formula for the lateral surface area (LSA) of a square - based pyramid.

The lateral surface area of a square - based pyramid is given by the formula \(LSA = 2\times s\times l\), where \(s\) is the length of the side of the square base and \(l\) is the slant height. For a square - based pyramid, there are 4 congruent triangular faces. The area of one triangular face is \(\frac{1}{2}\times s\times l\), so the area of 4 triangular faces (lateral surface area) is \(4\times\frac{1}{2}\times s\times l=2\times s\times l\). In the case of a square base with side length \(s\) and slant height \(l\), we can also think of it as the sum of the areas of the 4 triangular lateral faces. Since the base is a square with side length \(s = 10\) ft and from the diagram, we can assume that the slant height (the height of each triangular face) is also \(10\) ft (because the given length in the diagram for the triangular face seems to be the slant height).

Step2: Calculate the area of one triangular face.

The area of a triangle is given by the formula \(A=\frac{1}{2}\times base\times height\). For each lateral triangular face, the base \(b = 10\) ft and the height (slant height) \(h = 10\) ft. So the area of one triangular face is \(\frac{1}{2}\times10\times10 = 50\) \(ft^{2}\).

Step3: Calculate the lateral surface area.

Since a square - based pyramid has 4 lateral triangular faces, the lateral surface area \(LSA=4\times\) (area of one triangular face). Substituting the area of one triangular face (\(50\) \(ft^{2}\)) into the formula, we get \(LSA = 4\times50=200\) \(ft^{2}\). We can also use the formula \(LSA = 2\times s\times l\), where \(s = 10\) ft and \(l = 10\) ft. Then \(LSA=2\times10\times10 = 200\) \(ft^{2}\).

Answer:

\(200\)