Can we show that the area of this hexagon is $2(x^2 + xy + y^2)$?
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Ref: R8987

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Diagram of a right-angled triangle, with the constructed squares and the resulting hexagon.

The lengths of the two smaller sides of a right-angled triangle are $x$ in. and $y$ in. A square is constructed on each side of the triangle and the exterior points of the squares are joined to form a hexagon as in the diagram above. Show that the area of the hexagon is $2(x^2 + xy + y^2)$ sq. in. Given that $x + y = 10$, determine the minimum area of the hexagon.

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Calculus meets Functions

Can we show that the area of this hexagon is $2(x^2 + xy + y^2)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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Can we show that the area of this hexagon is $2(x^2 + xy + y^2)$?
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