AI generatedGeometry and measuresGCSE Higher / IGCSE Extended

Pythagoras with exact surd lengths

Pythagoras with exact surd lengths.

  • Split a compound solid into familiar shapes.
  • Use perpendicular height for volume and slant height for a cone’s curved area.
  • Add volumes, or subtract a removed part. Give cubic units.

Example 1

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.

Example 2

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.

Your turn

Question 1

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Check answer
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.
Question 2

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Check answer
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.
Question 3

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Check answer
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.
Question 4

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Check answer
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.
Question 5

Find in exact form. Lengths are in cm.

Geometry diagramABCDiagram not to scale
Check answer
Use Pythagoras: the hypotenuse squared equals the sum of the other squares.Take the positive root; simplify any square factor.
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