Question

What is the total area of the regular pyramid?

a) ( left( 1/2 ⋅ Perimeter of base ⋅ Slant height right) + left( Base area right) )
b) ( left( 1/2 ⋅ Perimeter of base ⋅ Height right) + left( Base area right) )
c) ( left( 1/3 ⋅ Perimeter of base ⋅ Slant height right) + left( Base area right) )
d) ( left( 1/3 ⋅ Perimeter of base ⋅ Height right) + left( Base area right) )

Answer 1

The total area of a regular pyramid is the sum of the lateral surface area, calculated by (1/2 × Perimeter of base × Slant height), and the base area. The correct formula is option a) (1/2 × Perimeter of base × Slant height) + (Base area).

Step-by-step explanation:

The total area of a regular pyramid is given by the formula for the lateral surface area plus the area of the base. The lateral surface area can be calculated as (1/2 × Perimeter of base × Slant height), and when you add the base area you get the total surface area of the pyramid. Therefore, the correct formula for the total area of a regular pyramid is:

a) (1/2 × Perimeter of base × Slant height) + (Base area)

This formula ensures that you are calculating the area of all the triangular sides (which form the lateral surface area of the pyramid) and the base area correctly. As for the other options provided in the question like option c and d, which involves dividing by 3, they are incorrect because they might be confusing the volume formula of the pyramid with the surface area formula.