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A trapezium has vertices at (–9, 3), (–9, 0), (–3, 6) and (–3, –3). It is enlarged by a scale factor of 2.6∙ Find the area of the enlarged trapezium.

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Answer:

Explanation:

To find the area of the enlarged trapezium, we first need to find the area of the original trapezium. The vertices of the original trapezium are (-9, 3), (-9, 0), (-3, 6), and (-3, -3) . Using the distance formula, we can find that the length of the top base is 6 units and the length of the bottom base is 9 units. The height of the trapezium is 9 units. Therefore, the area of the original trapezium is:

Area = (1/2) x (6 + 9) x 9

= 67.5 square units

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To find the area of the enlarged trapezium, we need to multiply the area of the original trapezium by the square of the scale factor. The scale factor is 2.6. Therefore, the area of the enlarged trapezium is:

Area = 67.5 x (2.6)^2

= 456.3 square units (rounded to one decimal place)

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Therefore, the area of the enlarged trapezium is approximately 456.3 square units.

I hope this helps! Let me know if you have any other questions or if there is anything else I can help you with.

User Edmond Wang
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