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The midpoints of the sides of a rectangle are joined by straight lines as shown - OCR - GCSE Maths - Question 13 - 2019 - Paper 1

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Question 13

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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=4abA = length \times width = 2a \times 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=12×A=12×4ab=2abArea_{shaded} = \frac{1}{2} \times A = \frac{1}{2} \times 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:

Percentageshaded=(AreashadedArea×100)=(2ab4ab×100)=50%Percentage_{shaded} = \left( \frac{Area_{shaded}}{Area} \times 100 \right) = \left( \frac{2ab}{4ab} \times 100 \right) = 50\%

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