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The shape below is formed by a rectangle of width 4 cm and a regular pentagon - OCR - GCSE Maths - Question 12 - 2021 - Paper 1
Question 12
The shape below is formed by a rectangle of width 4 cm and a regular pentagon. For the rectangle, the ratio of the width to the length is 2 : 5. Work out the perime... show full transcript
Worked Solution & Example Answer:The shape below is formed by a rectangle of width 4 cm and a regular pentagon - OCR - GCSE Maths - Question 12 - 2021 - Paper 1
Step 1
Calculate the Length of the Rectangle
Answer
Given the width of the rectangle is 4 cm and the ratio of the width to the length is 2 : 5, we can set up the following proportion:
Let the length be represented as (L).
[ \frac{4}{L} = \frac{2}{5} ]
Cross-multiplying gives:
[ 2L = 4 \times 5 ]
[ 2L = 20 ]
Dividing both sides by 2:
[ L = 10 \text{ cm} ]
Thus, the length of the rectangle is 10 cm.
Step 2
Step 3
Calculate the Perimeter of the Regular Pentagon
Answer
A regular pentagon has 5 equal sides. The side length needs to be calculated based on the width of the rectangle, which is also the height of the pentagon in this case.
Since each side of the pentagon corresponds to the width of 4 cm, the total perimeter of the regular pentagon is:
[ P_{pentagon} = 5 \times 4 = 20 \text{ cm} ]
Step 4
Calculate the Total Perimeter of the Shape
Answer
Finally, to find the total perimeter of the combined shape, we add the perimeter of the rectangle and the perimeter of the pentagon:
[ \text{Total Perimeter} = P_{rectangle} + P_{pentagon} ]
[ \text{Total Perimeter} = 28 + 20 = 48 \text{ cm} ]