2. jason has to mow the following shaded areas. if he is paid 20 cents per square metre, what is the costs of mowing the lawns?

3. find the area of the shaded region.
(a)
(b)

4. if each side of a rectangle is increased by 40%, what is the percentage increase in the area of the rectangle?

Question

2. jason has to mow the following shaded areas. if he is paid 20 cents per square metre, what is the costs of mowing the lawns?

3. find the area of the shaded region.
(a)
(b)

4. if each side of a rectangle is increased by 40%, what is the percentage increase in the area of the rectangle?

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of Composite Figures" ], "new_concepts": [ "Parallelogram Area", "Percentage Area Change" ], "current_concepts": [ "Area of Composite Figures", "Parallelogram Area", "Percentage Area Change" ] } ## Calculate the cost of mowing the lawns in Question 2 $$ \begin{aligned} &\text{Total Area} = \text{Area of Parallelogram} - 2 \times \text{Area of Unshaded Rectangles}\ &\text{Area of Parallelogram} = 19\text{ m} \times 22\text{ m} = 418\text{ m}^2\ &\text{Area of Unshaded Rectangles} = 2 \times (4\text{ m} \times 22\text{ m}) = 176\text{ m}^2\ &\text{Shaded Area} = 418\text{ m}^2 - 176\text{ m}^2 = 242\text{ m}^2\ &\text{Total Cost} = 242\text{ m}^2 \times \$0.20/\text{m}^2 = \$48.40 \end{aligned} $$ ## Find the shaded areas in Question 3 $$ \begin{aligned} &\text{Part (A):}\ &\text{Area of Parallelogram} = 15\text{ cm} \times 12\text{ cm} = 180\text{ cm}^2\ &\text{Area of Unshaded Rectangle} = 7\text{ cm} \times 8\text{ cm} = 56\text{ cm}^2\ &\text{Shaded Area (A)} = 180\text{ cm}^2 - 56\text{ cm}^2 = 124\text{ cm}^2\ \ &\text{Part (B):}\ &\text{Area of Large Triangle} = \frac{1}{2} \times 64\text{ mm} \times 26\text{ mm} = 832\text{ mm}^2\ &\text{Area of Unshaded Rectangle} = 16\text{ mm} \times 19\text{ mm} = 304\text{ mm}^2\ &\text{Shaded Area (B)} = 832\text{ mm}^2 - 304\text{ mm}^2 = 528\text{ mm}^2 \end{aligned} $$ ## Calculate the percentage increase in area for Question 4 $$ \begin{aligned} &\text{Let original dimensions be } l \text{ and } w.\ &\text{Original Area } A_1 = l \times w\ &\text{New dimensions: } 1.4l \text{ and } 1.4w\ &\text{New Area } A_2 = 1.4l \times 1.4w = 1.96(l \times w) = 1.96 A_1\ &\text{Percentage Increase} = (1.96 - 1) \times 100\% = 96\% \end{aligned} $$ ## Question 2 The cost of mowing the lawns is \$48.40. ## Question 3 (A) The area of the shaded region is $124\text{ cm}^2$. (B) The area of the shaded region is $528\text{ mm}^2$. ## Question 4 The percentage increase in the area of the rectangle is $96\%$. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the cost of mowing the lawns in Question 2

Find the shaded areas in Question 3

Calculate the percentage increase in area for Question 4

Answer:

Question 2

Question 3

Question 4