question 13 of 25

what is the area of the polygon below?

a. 111 square units
b. 120 square units
c. 147 square units
d. 156 square units

Question

question 13 of 25

what is the area of the polygon below?

a. 111 square units
b. 120 square units
c. 147 square units
d. 156 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": [ "Rectangle Area Formula", "Decomposition of Polygons" ], "new_concepts": [], "current_concepts": [ "Rectangle Area Formula", "Decomposition of Polygons", "Polygon Area Definition" ] } ## Calculate the area of the bounding rectangle $$ A_{\text{total}} = 13 \times 12 = 156 $$ ## Determine the dimensions of the missing corner region $$ \begin{aligned} w_{\text{missing}} &= 13 - 10 = 3 \ h_{\text{missing}} &= 12 - (12 - h_{\text{missing}}) \ \text{Vertical segments} &= 3 \text{ (given)} \ A_{\text{missing}} &= 3 \times 3 = 9 \end{aligned} $$ ## Subtract the missing area from the bounding rectangle $$ A_{\text{polygon}} = 156 - 9 = 147 $$

A. 111 square units

B. 120 square units

C. 147 square units

D. 156 square units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Decomposition of Polygons" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the area of the bounding rectangle

Determine the dimensions of the missing corner region

Subtract the missing area from the bounding rectangle

Answer: