Review question

# 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

Ref: R8987

## Question

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.