Question

a. sketch a net for this square pyramid and label the known lengths. draw in the box. b. find the surface area of the pyramid if unclear units. type your answer in the box. unclear square units show your reasoning. draw on the image select t to type

Explanation:

Step1: Identify the components of the net

The net of a square - pyramid consists of a square base and 4 congruent triangular faces.

Step2: Find the area of the base

Let the side - length of the square base be \(s\). The area of the square base \(A_{base}=s^{2}\).

Step3: Find the area of one triangular face

The area of a triangle is \(A_{triangle}=\frac{1}{2}bh\), where \(b\) is the base of the triangle (equal to the side - length of the square base \(s\)) and \(h\) is the slant height of the pyramid.

Step4: Find the total surface area

The total surface area \(A = A_{base}+4A_{triangle}=s^{2}+4\times\frac{1}{2}sh=s^{2} + 2sh\).

Since the side - length of the base \(s = 4\) (from the figure, assume the slant height \(h\) is known, if not given we cannot calculate a numerical value). If the slant height \(h\) is known, for example, if \(h = 5\):
\[

$$\begin{align*} A&=4^{2}+2\times4\times5\\ &=16 + 40\\ &=56 \end{align*}$$

\]

Answer:

If the side - length of the base \(s = 4\) and slant height \(h = 5\), the surface area is 56 square units. (Note: You need to substitute the actual values of the side - length of the base and slant height given in the problem to get the accurate answer).