Question

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b. find the surface area of the pyramid in square units. type your answer in the box. ( ) square units show your reasoning. draw on the image. select t to type.

Explanation:

Step1: Identify the base and lateral - faces

The pyramid has a square base and 4 triangular lateral - faces. Assume the side length of the square base is $s$ and the height of each triangular face (slant height) is $l$.

Step2: Calculate the area of the base

The area of a square base $A_{base}=s^{2}$.

Step3: Calculate the area of one triangular face

The area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. For the lateral - triangular faces of the pyramid, if the base of the triangle is the side of the square base $s$ and the height is the slant height $l$, then $A_{triangle}=\frac{1}{2}sl$.

Step4: Calculate the total surface area

The total surface area $A$ of the pyramid is the sum of the area of the base and the areas of the 4 lateral - faces. So $A = s^{2}+4\times\frac{1}{2}sl=s^{2} + 2sl$.

However, since no side - length or height values are given in the problem, we can't give a numerical answer. If we assume the side - length of the base $s = a$ units and slant height $l=b$ units, then the surface area $A=a^{2}+2ab$ square units.

Answer:

Since no specific values for the side - length of the base and the slant height are given, a general formula for the surface area of the square - based pyramid is $s^{2}+2sl$ square units, where $s$ is the side - length of the square base and $l$ is the slant height of the triangular faces.