1. find the area.
answer:

2. find the area.
answer:

3. $-2 \sqrt{5} + 3 \sqrt{5} =$
answer:

4. $6 \sqrt{3} - 2 \sqrt{3} =$
answer:

Question

1. find the area.
answer:

2. find the area.
answer:

3. $-2 \sqrt{5} + 3 \sqrt{5} =$
answer:

4. $6 \sqrt{3} - 2 \sqrt{3} =$
answer:

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Integer Arithmetic", "Signed Numbers" ], "new_concepts": [ "Area of Rectangle", "Area of Triangle", "Radical Operations" ], "current_concepts": [ "Area of Rectangle", "Area of Triangle", "Radical Operations", "Integer Arithmetic", "Signed Numbers" ] } ## Calculate the area of the rectangle The area of a rectangle is given by multiplying its length and width. $$ \begin{aligned} \text{Area} &= \text{length} \times \text{width} \ \text{Area} &= 5.2\text{ m} \times 3\text{ m} \ \text{Area} &= 15.6\text{ m}^2 \end{aligned} $$ ## Calculate the area of the triangle The area of a triangle is calculated using half the product of its base and height. $$ \begin{aligned} \text{Area} &= \frac{1}{2} \times \text{base} \times \text{height} \ \text{Area} &= \frac{1}{2} \times 6\text{ cm} \times 4.5\text{ cm} \ \text{Area} &= 3 \times 4.5 \ \text{Area} &= 13.5\text{ cm}^2 \end{aligned} $$ ## Simplify the first radical expression Using the **Signed Numbers** and **Integer Arithmetic** knowledge points $$ \begin{aligned} -2\sqrt{5} + 3\sqrt{5} &= (-2 + 3)\sqrt{5} \ &= 1\sqrt{5} \ &= \sqrt{5} \end{aligned} $$ ## Simplify the second radical expression Using the **Integer Arithmetic** knowledge point $$ \begin{aligned} 6\sqrt{3} - 2\sqrt{3} &= (6 - 2)\sqrt{3} \ &= 4\sqrt{3} \end{aligned} $$ ## Question 1 $15.6\text{ m}^2$ ## Question 2 $13.5\text{ cm}^2$ ## Question 3 $\sqrt{5}$ ## Question 4 $4\sqrt{3}$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Area of 2D Shapes" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the area of the rectangle

Calculate the area of the triangle

Simplify the first radical expression

Simplify the second radical expression

Answer:

Question 1

Question 2

Question 3

Question 4