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Question 7

$$ABCD$$ is a square. $$E$$ is one fourth of the way from $$A$$ to $$B$$ and $$F$$ is one fourth of the way from $$B$$ to C. $$X$$ is the centre of the square. Side of the square is 8 cm. Then the area of the shaded region in the figure in $$\text{cm}^2$$ is

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Solution

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Placing $$A=(0,8)$$, $$B=(8,8)$$, $$C=(8,0)$$, $$D=(0,0)$$ gives $$E=(2,8)$$, $$F=(8,6)$$ and $$X=(4,4)$$. Applying the shoelace formula to the quadrilateral $$E, B, F, X$$ gives an area of 16.

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