Question

question 7 (types of area mc) (multiple choice worth 1 points) a regular octagonal pyramid has side lengths of 11 inches, a slant height of 17 inches, and an apothem of 13.278 inches. what is the surface area of the pyramid? 2,080.24 in² 9,931.94 in² 748 in² 1,332.23 in² question 8 (multiple choice worth 1 points) (an interest in growth models lc)

Explanation:

Step1: Calculate the perimeter of the base

The base is a regular octagon with side length \(s = 11\) inches. The perimeter \(P\) of a regular octagon is \(P=8s\).

$$P = 8\times11=88\space\text{in}$$

Step2: Calculate the area of the base

The formula for the area of a regular polygon is \(A_{base}=\frac{1}{2}Pa\), where \(P\) is the perimeter and \(a\) is the apothem. Given \(a = 13.278\) inches and \(P = 88\) inches.

$$A_{base}=\frac{1}{2}\times88\times13.278= 584.232\space\text{in}^2$$

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a pyramid is \(A_{lateral}=\frac{1}{2}Pl\), where \(P\) is the perimeter and \(l\) is the slant height. Given \(l = 17\) inches and \(P = 88\) inches.

$$A_{lateral}=\frac{1}{2}\times88\times17 = 748\space\text{in}^2$$

Step4: Calculate the total surface area

The total surface area \(A_{total}=A_{base}+A_{lateral}\)

$$A_{total}=584.232 + 748=1332.232\approx1332.23\space\text{in}^2$$

Answer:

\(1332.23\space\text{in}^2\)