To find the total surface area of the pyramid, we need to calculate the area of the base and the area of the four triangular faces.
Step 1: Calculate the area of the base
The base of the pyramid is a square with each side measuring 8 units. The area of a square is calculated using the formula:
Area = side × side
So, the area of the base is:
Area of base = 8 × 8 = 64 square units
Step 2: Calculate the area of one triangular face
Each triangular face has a base of 8 units (the same as the side of the square) and a slant height of 5 units. The area of a triangle is calculated using the formula:
Area = 1/2 × base × height
In this case, the base of the triangle is 8 and the height is the slant height, which is 5:
Area of one triangle = 1/2 × 8 × 5 = 20 square units
Step 3: Calculate the total area of the four triangular faces
Since there are four triangular faces, we multiply the area of one triangle by 4:
Total area of triangular faces = 4 × 20 = 80 square units
Step 4: Calculate the total surface area of the pyramid
Finally, we add the area of the base to the total area of the triangular faces to get the total surface area:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 64 + 80 = 144 square units
Therefore, the total surface area of the pyramid is 144 square units.