question 1 of 10

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

a. 5545 square units
b. 1572 square units
c. 2772 square units
d. 792 square units

Question

question 1 of 10

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

a. 5545 square units
b. 1572 square units
c. 2772 square units
d. 792 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": [ "Polygon Area Definition" ], "new_concepts": [ "Regular Polygon Area", "Apothem" ], "current_concepts": [ "Polygon Area Definition", "Regular Polygon Area", "Apothem" ] } ## Identify the given parameters of the regular heptagon $$ \begin{aligned} &n = 7 \quad \text{(number of sides)} \ &s = 20.8 \quad \text{(side length)} \ &a = 21.6 \quad \text{(apothem)} \end{aligned} $$ ## Calculate the perimeter of the heptagon $$ P = n \cdot s = 7 \cdot 20.8 = 145.6 $$ ## Calculate the area of the regular heptagon $$ \begin{aligned} &A = \frac{1}{2} \cdot P \cdot a \ &A = \frac{1}{2} \cdot 145.6 \cdot 21.6 \ &A = 1572.48 \approx 1572 \text{ square units} \end{aligned} $$

A. 5545 square units

B. 1572 square units

C. 2772 square units

D. 792 square units

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

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters of the regular heptagon

Calculate the perimeter of the heptagon

Calculate the area of the regular heptagon

Answer: