question 10 of 10

to the nearest square unit, what is the area of the regular octagon shown below?

a. 349 square units
b. 698 square units
c. 1395 square units
d. 2791 square units

Question

question 10 of 10

to the nearest square unit, what is the area of the regular octagon shown below?

a. 349 square units
b. 698 square units
c. 1395 square units
d. 2791 square units

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 $$ \begin{aligned} n &= 8 \ s &= 17 \ P &= n \times s = 8 \times 17 = 136 \end{aligned} $$ ## Calculate the area using the apothem and perimeter $$ \begin{aligned} a &= 20.52 \ A &= \frac{1}{2} \times a \times P \ A &= \frac{1}{2} \times 20.52 \times 136 \ A &= 10.26 \times 136 = 1395.36 \end{aligned} $$ ## Round to the nearest square unit $$ A \approx 1395 \text{ square units} $$

(A) 349 square units

(B) 698 square units

(C) 1395 square units

(D) 2791 square units

{ "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 and perimeter

Round to the nearest square unit

Answer: