the area of the regular pentagon is $6.9\text{ cm}^2$.

what is the perimeter?

$2\text{ cm}$
$5\text{ cm}$
$10\text{ cm}$
$20\text{ cm}$

Question

the area of the regular pentagon is $6.9\text{ cm}^2$.

what is the perimeter?

$2\text{ cm}$
$5\text{ cm}$
$10\text{ cm}$
$20\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of Regular Polygon", "Apothem of a Regular Polygon" ], "new_concepts": [], "current_concepts": [ "Area of Regular Polygon", "Apothem of a Regular Polygon", "Regular Pentagon Properties" ] } ## Identify the given values and formula $$ \begin{aligned} A &= 6.9\text{ cm}^2 \ a &= 1.38\text{ cm} \ A &= \frac{1}{2} a P \end{aligned} $$ ## Solve for the perimeter $$ \begin{aligned} 6.9 &= \frac{1}{2} (1.38) P \ 6.9 &= 0.69 P \ P &= \frac{6.9}{0.69} = 10\text{ cm} \end{aligned} $$

(A) 2 cm

(B) 5 cm

(C) 10 cm

(D) 20 cm

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Solve for the perimeter

Answer: