To find the lateral and total surface area of a pyramid, we first need to understand the basic formulas involved.
Lateral Surface Area
The lateral surface area (LSA) of a pyramid is the sum of the areas of its triangular faces. The formula for the lateral surface area of a pyramid can be expressed as:
LSA = (1/2) × Perimeter of Base × Slant Height
where the perimeter of the base is the total length around the base of the pyramid, and the slant height is the height of the triangular face from the base to the apex.
Total Surface Area
The total surface area (TSA) of a pyramid includes the lateral surface area plus the area of the base. The formula for the total surface area is:
TSA = LSA + Area of Base
Example Calculation
Let’s say we have a square pyramid with a base side length of 4 cm and a slant height of 5 cm.
- Step 1: Calculate the Perimeter of the Base:
Perimeter = 4 sides × 4 cm = 16 cm. - Step 2: Calculate the Lateral Surface Area:
LSA = (1/2) × 16 cm × 5 cm = 40 cm². - Step 3: Calculate the Area of the Base:
Area of Base = 4 cm × 4 cm = 16 cm². - Step 4: Calculate the Total Surface Area:
TSA = 40 cm² + 16 cm² = 56 cm².
Thus, the lateral surface area of the pyramid is 40 cm², and the total surface area is 56 cm².