find the area of the figure. (sides meet at right angles.)

$\square\text{ yd}^2$

Question

find the area of the figure. (sides meet at right angles.)

$\square\text{ yd}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Area of Composite Figures", "Area of Rectangles" ], "new_concepts": [], "current_concepts": [ "Area of Composite Figures", "Area of Rectangles" ] } ## Determine the dimensions of the decomposed rectangles $$ \begin{aligned} &\text{Top Rectangle:} \ &\text{Width} = 3\text{ yd} + 4\text{ yd} + 3\text{ yd} = 10\text{ yd} \ &\text{Height} = 3\text{ yd} \ \ &\text{Bottom Rectangle:} \ &\text{Width} = 4\text{ yd} \ &\text{Height} = 2\text{ yd} \end{aligned} $$ ## Calculate the area of each rectangle $$ \begin{aligned} &\text{Area}_{\text{top}} = 10\text{ yd} \times 3\text{ yd} = 30\text{ yd}^2 \ &\text{Area}_{\text{bottom}} = 4\text{ yd} \times 2\text{ yd} = 8\text{ yd}^2 \end{aligned} $$ ## Sum the areas to find the total area $$ \text{Total Area} = 30\text{ yd}^2 + 8\text{ yd}^2 = 38\text{ yd}^2 $$ Find the area of the figure. (Sides meet at right angles.) 38 $\text{yd}^2$ { "elements": [ { "type": "polygon", "params": [ [-5, 3], [5, 3], [5, 0], [2, 0], [2, -2], [-2, -2], [-2, 0], [-5, 0] ], "properties": { "fillColor": "rgba(140, 85, 242, 0.3)", "strokeColor": "#8C55F2", "strokeWidth": 2, "withLabel": false } }, { "type": "segment", "params": [ [-2, 0], [2, 0] ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 1, "dash": 2 } }, { "type": "text", "params": [ [-5.6, 1.5], "3 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [5.2, 1.5], "3 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [-3.5, 0.3], "3 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [3.5, 0.3], "3 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [-2.5, -1], "2 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [2.1, -1], "2 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [0, -2.5], "4 yd" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [0, 1.2], "Area = 30" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ [0, -1], "Area = 8" ], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine the dimensions of the decomposed rectangles

Calculate the area of each rectangle

Sum the areas to find the total area

Answer: