The total surface area of the pyramid is 52 square units
The formula for calculating the area of the triangular based pyramid is expressed as;
[tex]TSA=Base \ Area+\frac{1}{2}ps[/tex] where;
p is the perimeter of the base
s is the slant height
Get the Base area
[tex]Base \ Area = \frac{1}{2}bh\\Base \ Area = \frac{1}{2}*6*\sqrt{5^2-3^2} \\ Base \ Area = \frac{1}{2}*6*\sqrt{25-9} \\ Base \ Area = \frac{1}{2}*6*\sqrt{16} \\ Base \ Area = \frac{1}{2}*6*4 \\ Base \ Area = \frac{24}{2} \\Base \ Area = 12 units^2[/tex]
Get the perimeter
Perimeter = 5 + 5 + 6
Perimeter = 16 units
Slant height = 5units
Substitute the given values into the formula above as shown;
[tex]TSA=12+\frac{1}{2}*16*5\\TSA=12+(8*5)\\\\TSA = 12 + 40\\TSA = 52 units ^2[/tex]
Hence the total surface area of the pyramid is 52 square units
Learn more here: https://brainly.com/question/23353623
