an equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. what is the area of the equilateral triangle, rounded to the nearest tenth?

- 2.7 cm^2
- 4.1 cm^2
- 16.2 cm^2
- 24.2 cm^2

Question

an equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. what is the area of the equilateral triangle, rounded to the nearest tenth?

- 2.7 cm^2
- 4.1 cm^2
- 16.2 cm^2
- 24.2 cm^2

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" ], "current_concepts": [ "Area of Regular Polygon", "Apothem", "Equilateral Triangle Properties" ] } ## Identify given values and formula $$ \begin{aligned} a &= 2.16\text{ cm} \ P &= 22.45\text{ cm} \ A &= \frac{1}{2} a P \end{aligned} $$ ## Calculate the area $$ \begin{aligned} A &= \frac{1}{2} \times 2.16 \times 22.45 \ A &= 1.08 \times 22.45 \ A &= 24.246\text{ cm}^2 \end{aligned} $$ ## Round to the nearest tenth $$ A \approx 24.2\text{ cm}^2 $$

(A) $2.7\text{ cm}^2$

(B) $4.1\text{ cm}^2$

(C) $16.2\text{ cm}^2$

(D) $24.2\text{ cm}^2$

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

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QUESTION IMAGE

Question

Explanation:

Identify given values and formula

Calculate the area

Round to the nearest tenth

Answer: