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# Rotation and Area

A has coordinates (4,4) and B is obtained by rotating A about the origin O through an angle of 135 ยบ anti-clockwise.

Calculate the area of triangle AOB.

*This problem is taken from the World Mathematics Championships*

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A has coordinates (4,4) and B is obtained by rotating A about the origin O through an angle of 135 ยบ anti-clockwise.

Calculate the area of triangle AOB.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.