find the area of the figure.

$\square\text{ m}^2$
(simplify your answer.)

Question

find the area of the figure.

$\square\text{ m}^2$
(simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Composite Area", "Trapezoid Area" ], "current_concepts": [ "Composite Area", "Trapezoid Area", "Area of Polygons" ] } ## Decompose the figure into a rectangle and a trapezoid $$ \begin{aligned} &\text{Rectangle dimensions: } \text{width} = 40\text{ m}, \text{height} = 80\text{ m}\ &\text{Trapezoid parallel bases: } b_1 = 40\text{ m}, b_2 = 170\text{ m}\ &\text{Trapezoid height: } h = 80\text{ m} - 30\text{ m} = 50\text{ m} \end{aligned} $$ ## Calculate the areas of the decomposed parts $$ \begin{aligned} &A_{\text{rectangle}} = 40 \times 30 = 1200\text{ m}^2\ &A_{\text{trapezoid}} = \frac{1}{2} \times (40 + 170) \times 50 = \frac{1}{2} \times 210 \times 50 = 5250\text{ m}^2 \end{aligned} $$ ## Sum the areas to find the total area $$ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{trapezoid}} = 1200 + 5250 = 6450\text{ m}^2 $$ Find the area of the figure. 6450 $\text{m}^2$ (Simplify your answer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Polygons" ] }

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QUESTION IMAGE

Question

Explanation:

Decompose the figure into a rectangle and a trapezoid

Calculate the areas of the decomposed parts

Sum the areas to find the total area

Answer: