what is the surface area of this triangular pyramid? square feet

Explanation:

Step1: Calculate base - area

The base is a triangle with base $b = 9$ ft and height $h = 7.8$ ft. The area of a triangle is $A_{base}=\frac{1}{2}\times b\times h$. So, $A_{base}=\frac{1}{2}\times9\times7.8 = 35.1$ square - feet.

Step2: Calculate area of one lateral face

One lateral face has base $b = 9$ ft and height $h = 7$ ft. The area of a triangle is $A_{lateral}=\frac{1}{2}\times b\times h$. So, $A_{lateral}=\frac{1}{2}\times9\times7 = 31.5$ square - feet.

Step3: Calculate total lateral - area

Since there are 3 lateral faces, the total lateral area $A_{lateral - total}=3\times A_{lateral}=3\times31.5 = 94.5$ square - feet.

Step4: Calculate surface area

The surface area $A$ of a triangular pyramid is the sum of the base area and the total lateral area. So, $A = A_{base}+A_{lateral - total}=35.1 + 94.5=129.6$ square - feet.

Answer:

129.6