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### Number and algebra

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# Diagonals for Area

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Age 16 to 18

Challenge Level

Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2