the area of the regular octagon is $10.15\text{ cm}^2$.

what is the measure of the apothem, rounded to the nearest hundredth of a centimeter?

$1.27\text{ cm}$
$1.75\text{ cm}$
$2.33\text{ cm}$
$2.54\text{ cm}$

Question

the area of the regular octagon is $10.15\text{ cm}^2$.

what is the measure of the apothem, rounded to the nearest hundredth of a centimeter?

$1.27\text{ cm}$
$1.75\text{ cm}$
$2.33\text{ cm}$
$2.54\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Area of Regular Polygon", "Apothem of Polygon" ], "current_concepts": [ "Area of Regular Polygon", "Apothem of Polygon" ] } ## Calculate the perimeter of the regular octagon $$ \begin{aligned} n &= 8 \ s &= 1.45\text{ cm} \ P &= n \cdot s = 8 \cdot 1.45 = 11.6\text{ cm} \end{aligned} $$ ## Relate area, perimeter, and apothem $$ \begin{aligned} A &= 10.15\text{ cm}^2 \ A &= \frac{1}{2} \cdot P \cdot a \end{aligned} $$ ## Solve for the apothem $$ \begin{aligned} 10.15 &= \frac{1}{2} \cdot 11.6 \cdot a \ 10.15 &= 5.8 \cdot a \ a &= \frac{10.15}{5.8} = 1.75\text{ cm} \end{aligned} $$

(A) 1.27 cm

(B) 1.75 cm

(C) 2.33 cm

(D) 2.54 cm

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

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QUESTION IMAGE

Question

Explanation:

Calculate the perimeter of the regular octagon

Relate area, perimeter, and apothem

Solve for the apothem

Answer: