question 24 of 25

a regular octagon with sides of length 11 and an apothem of length 8.85 has an area of ____ square units.

a. 121
b. 389.40
c. 778.80
d. 430.77
e. 98.65
f. 97.35

Question

question 24 of 25

a regular octagon with sides of length 11 and an apothem of length 8.85 has an area of ____ square units.

a. 121
b. 389.40
c. 778.80
d. 430.77
e. 98.65
f. 97.35

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Regular Polygon Area", "Apothem", "Perimeter of Polygons" ], "new_concepts": [], "current_concepts": [ "Regular Polygon Area", "Apothem", "Perimeter of Polygons" ] } ## Calculate the perimeter of the regular octagon $$ \begin{aligned} n &= 8 \ s &= 11 \ P &= n \cdot s = 8 \cdot 11 = 88 \end{aligned} $$ ## Calculate the area using the apothem formula $$ \begin{aligned} a &= 8.85 \ A &= \frac{1}{2} \cdot P \cdot a \ A &= \frac{1}{2} \cdot 88 \cdot 8.85 \ A &= 44 \cdot 8.85 = 389.40 \end{aligned} $$

A. 121

B. 389.40

C. 778.80

D. 430.77

E. 98.65

F. 97.35

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Regular Polygon Area" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the perimeter of the regular octagon

Calculate the area using the apothem formula

Answer: