Question

a regular triangular pyramid has a base perimeter of 13.5 units, a base area of approximately 8.8 square units, and a slant height of 6 units. which expression represents the approximate surface area, in square units, of the pyramid? options: (\frac{1}{2}(8.8)(6)), (\frac{1}{2}(13.5)(6)), (8.8 + \frac{1}{2}(13.5)(6)), (13.5 + \frac{1}{2}(8.8)(6))

Explanation:

Step1: Recall Surface Area of Pyramid

The surface area \( SA \) of a regular pyramid is the sum of the base area (\( B \)) and the lateral surface area (\( LSA \)). The formula for lateral surface area of a regular pyramid is \( LSA=\frac{1}{2}Pl \), where \( P \) is the base perimeter and \( l \) is the slant height. So \( SA = B+\frac{1}{2}Pl \).

Step2: Identify Given Values

From the problem, base area \( B \approx 8.8 \) square units, base perimeter \( P = 13.5 \) units, slant height \( l = 6 \) units.

Step3: Substitute into Formula

Substitute \( B = 8.8 \), \( P = 13.5 \), and \( l = 6 \) into \( SA = B+\frac{1}{2}Pl \). We get \( SA=8.8+\frac{1}{2}(13.5)(6) \).

Answer:

\( 8.8 + \frac{1}{2}(13.5)(6) \) (corresponding to the third option, assuming the options are labeled with the third one as \( 8.8+\frac{1}{2}(13.5)(6) \))