there is a pair of parallel sides in the following shape. what is the area of the shape? \text{______} \text{ units}^2

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Trapezoid Area", "Geometric Decomposition" ], "current_concepts": [ "Trapezoid Area", "Geometric Decomposition" ] } ## Identify the geometric properties of the shape $$ \begin{aligned} &\text{Parallel sides (bases): } b_1 = 6, \quad b_2 = 8 \ &\text{Perpendicular distance (height): } h = 4 \end{aligned} $$ ## Apply the area formula for a trapezoid $$ \begin{aligned} &A = \frac{b_1 + b_2}{2} \cdot h \ &A = \frac{6 + 8}{2} \cdot 4 \end{aligned} $$ ## Calculate the final area $$ \begin{aligned} &A = 7 \cdot 4 \ &A = 28 \end{aligned} $$ There is a pair of parallel sides in the following shape. What is the area of the shape? 28 units$^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Trapezoid Area" ] }

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Explanation:

Identify the geometric properties of the shape

Apply the area formula for a trapezoid

Calculate the final area

Answer: