calculating the perimeter of a rhombus

the vertices of rhombus defg are d(1, 4), e(4, 0), f(1, -4), and g(-2, 0).

what is the perimeter of the rhombus?

units

Question

calculating the perimeter of a rhombus

the vertices of rhombus defg are d(1, 4), e(4, 0), f(1, -4), and g(-2, 0).

what is the perimeter of the rhombus?

units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Rhombus Properties" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Rhombus Properties", "Perimeter of a Rhombus" ] } ## Calculate the length of one side Using the *Distance Formula* knowledge point $$ \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\ DE &= \sqrt{(4 - 1)^2 + (0 - 4)^2}\ DE &= \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \end{aligned} $$ ## Calculate the perimeter of the rhombus Using the *Rhombus Properties* knowledge point $$ \begin{aligned} P &= 4 \times s\ P &= 4 \times 5 = 20 \end{aligned} $$ The vertices of rhombus DEFG are D(1, 4), E(4, 0), F(1, -4), and G(-2, 0). What is the perimeter of the rhombus? 20 units { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter of a Rhombus" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the length of one side

Calculate the perimeter of the rhombus

Answer: