Question

find the surface area of a square pyramid with side length 1 in and slant height 4 in. answer attempt 1 out of 2 in² submit answer

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 1\) in. The area of a square is \(A_{base}=s^{2}\).

$$A_{base}=1^{2}=1$$

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 \(s = 1\) in and the height is the slant height \(l = 4\) in.

$$A_{\triangle}=\frac{1}{2}\times1\times4 = 2$$

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=4\times A_{\triangle}\)

$$A_{triangles}=4\times2=8$$

Step4: Calculate the total surface area

The total surface area \(A\) of the square pyramid is the sum of the base area and the area of the four triangular faces. \(A=A_{base}+A_{triangles}\)

$$A = 1+8=9$$

Answer:

\(9\)