The given pyramid's total surface area is 3. 24.0 square feet.
Step-by-step explanation:
Step 1:
To calculate the surface area of the given figure, we need to find the surface areas of the different shapes in the figure.
There are 3 triangles and 1 square in the figure.
Step 2:
All the triangles are similar.
The surface area of a triangle = [tex]\frac{1}{2} (baselength)(height).[/tex]
The similar triangles have a base length of 3 feet and a height of 2.5 feet.
The surface area of 1 similar triangle = [tex]\frac{1}{2} (3)(2.5)= 3.75[/tex] square feet.
The surface area for all the similar triangles = [tex]3.75 (4) = 15[/tex] square feet.
Step 3:
The surface area of a square is the square of its side length. The square has a side length of 3 feet.
The surface area of the square = [tex]a^{2} = 3^{2} =9[/tex] square feet.
Step 4:
To calculate the total surface area we sum up all the individual surface area.
The total surface area = [tex]15 + 9 = 24[/tex] square feet which is the third option.
