Rectangle in a quarter circle
A rectangle sits in the corner of a quarter circle, one corner at the centre and the opposite corner on the curved edge. The student finds the length of the rectangle's other diagonal, works out the radius first from two pieces of the bottom edge, or finds the perimeter of the triangle the diagonal cuts off.
It looks as if it needs the rectangle's sides, but it doesn't. The other diagonal runs from the centre to the curve, so it is a radius, and a rectangle's two diagonals are the same length. Some questions give a number that isn't needed, so the student has to see which ones matter.
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What changes each time
- A plain diagram in cm, or a garden with a vegetable patch in m
- The radius given, or found from two pieces
- The diagonal itself, or the perimeter of a triangle
More shapes and angles practice
- Sides and corners of 2D shapes (Grade 2)
- Faces, edges and vertices (Grade 3)
- Sorting quadrilaterals (Grade 3)
- Turning and flipping letters (Grade 3)
- Counting squares of every size (Grade 3)
- Inside or outside the loop (Grade 3)
- Which piece fills the gap? (Grade 3)
- Symmetry on a grid (Grade 4)
- Rotations and reflections (Grade 4)
- Reading a protractor (Grade 4)
- Parallel and perpendicular lines (Grade 4)
- Parts of a circle (Grade 4)
- Draw without lifting your pencil (Grade 4)
- Can these sticks make a triangle? (Grade 4)
- 3D shapes: side view (Grade 5)
- Painted cube puzzle (Grade 5)
- Rope around the Earth (Grade 5)
- Can dominoes cover the board? (Grade 5)
- Angles in a circle (Grade 6)
- Inscribed circle in a right triangle (Grade 8)