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A shape is drawn on a one-centimetre grid - OCR - GCSE Maths - Question 5 - 2019 - Paper 1

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Question 5

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A shape is drawn on a one-centimetre grid. (a) Find the perimeter of the shape. (b) How many lines of symmetry does the shape have?

Worked Solution & Example Answer:A shape is drawn on a one-centimetre grid - OCR - GCSE Maths - Question 5 - 2019 - Paper 1

Step 1

Find the perimeter of the shape.

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Answer

To find the perimeter of the shape, we need to sum the length of all the outer edges.

  1. The shape consists of four rectangles. Count the lengths of each side:

    • The top side of the main rectangle is 2 cm wide.
    • The two vertical sides on either end total 4 cm (2 cm on each side).
    • The bottom side is 4 cm wide (2 cm on each end and 2 cm in the middle).
  2. Now, adding these lengths together:

    • Top side: 2 cm
    • Right vertical side: 2 cm
    • Bottom side: 4 cm
    • Left vertical side: 2 cm

    Thus, the total perimeter is:

    P=2+2+4+2=10P = 2 + 2 + 4 + 2 = 10

    So, the perimeter of the shape is 10 cm.

Step 2

How many lines of symmetry does the shape have?

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Answer

The shape has 2 lines of symmetry:

  1. One vertical line of symmetry that divides the shape into two equal halves.
  2. One horizontal line of symmetry that also divides the shape into two equal halves.

Thus, the shape has a total of 2 lines of symmetry.

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