your answer to the nearest hundredth.

12.64
18.96
25.28
26.78

Question

your answer to the nearest hundredth.

12.64
18.96
25.28
26.78

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Coordinate Distance", "Polygon Perimeter" ], "new_concepts": [], "current_concepts": [ "Coordinate Distance", "Polygon Perimeter" ] } ## Identify the coordinates of the vertices Using the *Coordinate Distance* knowledge point $$ \begin{aligned} A &= (-4, 0) \ B &= (2, 2) \ C &= (1, 5) \ D &= (-5, 3) \end{aligned} $$ ## Calculate the lengths of the four sides Using the *Coordinate Distance* knowledge point $$ \begin{aligned} AB &= \sqrt{(2 - (-4))^2 + (2 - 0)^2} = \sqrt{6^2 + 2^2} = \sqrt{40} \approx 6.3246 \ BC &= \sqrt{(1 - 2)^2 + (5 - 2)^2} = \sqrt{(-1)^2 + 3^2} = \sqrt{10} \approx 3.1623 \ CD &= \sqrt{(-5 - 1)^2 + (3 - 5)^2} = \sqrt{(-6)^2 + (-2)^2} = \sqrt{40} \approx 6.3246 \ DA &= \sqrt{(-4 - (-5))^2 + (0 - 3)^2} = \sqrt{1^2 + (-3)^2} = \sqrt{10} \approx 3.1623 \end{aligned} $$ ## Calculate the perimeter of the quadrilateral Using the *Polygon Perimeter* knowledge point $$ \begin{aligned} P &= AB + BC + CD + DA \ P &= \sqrt{40} + \sqrt{10} + \sqrt{40} + \sqrt{10} \ P &= 2\sqrt{40} + 2\sqrt{10} \ P &\approx 2(6.3246) + 2(3.1623) = 12.6492 + 6.3246 = 18.9738 \approx 18.97 \end{aligned} $$ Comparing with the given options, $18.96$ is the closest value (derived from $2 \times 6.32 + 2 \times 3.16 = 12.64 + 6.32 = 18.96$).

(A) 12.64

(B) 18.96

(C) 25.28

(D) 26.78

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

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the vertices

Calculate the lengths of the four sides

Calculate the perimeter of the quadrilateral

Answer: