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Resizing 2D Shapes

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Resizing 2D Shapes

A local park is updating its signs. You will resize 2D shapes to make a small sign fit a larger display. Use scale factors to calculate side lengths, perimeter and area. Show your working where asked.

Part A: Plan the sign

The park's small sign has a 5 cm by 3 cm rectangular panel. Its border is a right-angled triangle with vertices A(0, 0), B(4, 0) and C(0, 3), measured in centimetres. Coordinates describe the shape fully.

1.The triangle border is enlarged by a scale factor of 2, centred at (0, 0). What are the new coordinates of A, B and C?
2.Which statements are true when a shape is resized by a scale factor of 2? Select all that apply.
  • Every side length doubles.
  • Every angle doubles.
  • The shape keeps its original proportions.
  • Its area doubles.
3.The rectangular panel measures 5 cm by 3 cm. Find its dimensions after an enlargement by scale factor 1.5.
4.A square badge has side length 8 cm. It is reduced by scale factor 0.5. What is the new side length?

Part B: Compare the resized designs

For these questions, remember that resizing multiplies each length by the scale factor, while area changes by the scale factor squared.

5.The original panel is 5 cm by 3 cm. Calculate its area, then calculate the area of the panel enlarged by scale factor 2.
6.A circular park marker has an area of 20 cm². Its design is enlarged by scale factor 3. What is the area of the enlarged marker?
7.The triangle border has side lengths 3 cm, 4 cm and 5 cm. Find its perimeter after it is enlarged by scale factor 2.
8.True or false? A shape enlarged by scale factor 4 has angles four times as large as the original angles. Explain your choice.
9.The original rectangular panel has perimeter 16 cm. What is the perimeter after it is enlarged by scale factor 1.5?
10.A designer says, “If a shape's side lengths are doubled, its area is doubled too.” Is the designer correct? Use the 5 cm by 3 cm panel to justify your answer.

2 printable pages

  • Resizing 2D Shapes, page 1 of 2: Part A: Plan the sign

    Page 1

  • Resizing 2D Shapes, page 2 of 2: Part B: Compare the resized designs

    Page 2

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