Let's apply the formula for the lateral area and total surface area of a pyramid.
• Lateral Surface Area:
To find the lateral area of a pyramid, apply the formula:
Where:
p is the perimeter of the base
s is the slant height.
Example:
From the above square base pyramid, we have:
length of base, b = 4 cm
Slant height, s = 3 cm
Let's find the lateral area.
Since the base is a square, the perimeter will be:
p = 4 x 4 = 16 cm
Hence, to find the lateral area, we have:
![\begin{gathered} A_l=(1)/(2)ps \\ \\ A_l=(1)/(2)*16*3 \\ \\ A_l=24\operatorname{cm}^2 \end{gathered}]()
Therefore, the lateral area of the square base pyramid above is 24 cm².
• Total surface area of a pyramid.
To find the total surface area of a pyramid, apply the formula:
Where:
A is the area of the base
p is the perimeter of the base
s is the slant height.
Or we can simply say, the formula for total surface area is:
Total surface area = Lateral area + Area of base
Example:
Using the squarea base pyramid above, we have:
Area of base = 4 x 4 = 16 cm²
Lateral area = 24 cm²
Total surface area = 24 cm² + 16 cm² = 40 cm².