The midpoints of the sides of a rectangle are joined by straight lines as shown - OCR - GCSE Maths - Question 13 - 2019 - Paper 1
Question 13
The midpoints of the sides of a rectangle are joined by straight lines as shown.
Work out the percentage of the rectangle that is shaded.
Worked Solution & Example Answer:The midpoints of the sides of a rectangle are joined by straight lines as shown - OCR - GCSE Maths - Question 13 - 2019 - Paper 1
Step 1
Work out the area of the rectangle
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Answer
Let the length of the rectangle be 2a and the width be 2b. Therefore, the area of the rectangle (A) can be calculated as:
A=length×width=2a×2b=4ab
Step 2
Calculate the area of the shaded region
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Answer
The shaded region is formed by connecting the midpoints of the rectangle. The area of this shaded region is half of the area of the rectangle, hence:
Areashaded=21×A=21×4ab=2ab
Step 3
Calculate the percentage shaded
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Answer
To find the percentage of the rectangle that is shaded, use the formula: