What is the total surface area of a pyramid with base equal to 8 m and height equal to 3 m?
Responses:
69 m²
64 m²
80 m²
144 m²
The total surface area of a pyramid can be calculated using the formula: Area of base + 1/2 * Perimeter of base * Slant height
First, calculate the area of the base:
Area of base = 8 m * 8 m = 64 m²
Next, calculate the slant height using the Pythagorean theorem:
Slant height = √( (Perpendicular height)² + (1/2 * Base)² )
Slant height = √(3² + (1/2 * 8)²)
Slant height = √(9 + 16)
Slant height = √25
Slant height = 5 m
Now, calculate the total surface area:
Total surface area = 64 m² + 1/2 * 8 m * 5 m = 64 m² + 20 m² = 84 m²
Therefore, the total surface area of the pyramid is 84 m². In the given options, the closest answer is 80 m².