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 in square units. type your answer in the box. show your reasoning. draw on the image. select t to type.

Explanation:

Step1: Identify parts of net

A net of a square - pyramid consists of a square base and 4 triangular faces. The base has side - length 4 (from the given pyramid), and the triangular faces have base 4 and height 7.

Step2: Calculate area of base

The area of the square base $A_{base}=s^2$, where $s = 4$. So $A_{base}=4^2=16$.

Step3: Calculate area of one triangular face

The area of a triangle is $A_{triangle}=\frac{1}{2}bh$, where $b = 4$ and $h = 7$. So $A_{triangle}=\frac{1}{2}\times4\times7 = 14$.

Step4: Calculate total surface area

The total surface area $A$ of the square - pyramid is the sum of the area of the base and the areas of the 4 triangular faces. $A=A_{base}+4A_{triangle}$. Substituting the values, we get $A = 16+4\times14=16 + 56=72$.

Answer:

72