Geometry Puzzles with Algebra GCSE Higher

Sixteen geometry problems where the lengths and angles are given in terms of x. Students form an equation from an area, perimeter, volume, angle fact, Pythagoras or similar triangles, then solve it. Stretch for students aiming at grades 8 and 9, full answers included.

Worksheet (2 pages): 8 problems, including a rectangle and a square with equal areas, a right-angled triangle from a ratio and its area, angles in a triangle leading to a quadratic, a cuboid from its volume, similar triangles, and a cylinder and cone with the same volume.

Further practice (2 pages): 8 harder problems, including an isosceles trapezium from a ratio, a cyclic quadrilateral, a sphere melted into a cylinder, a rhombus from its diagonals, an equilateral triangle and answers given as surds or in terms of x.

Answers to all 16 problems are included as a separate file.

Suitable for GCSE Higher (AQA A18, G16, G17 and G20) as stretch for top sets or as revision for students aiming at the top grades.

AI was used to help create this resource, working from my own lesson design.