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# Angles, Polygons and Geometrical Proof Short Problems

### Griddy Region

### Garden Fence

### Overlapping Annuli

### Altitude Inequalities

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This is part of our collection of Short Problems.

You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ | Sheet 1 | Solutions |

Sheet 2 | Solutions | |

Sheet 3 | Solutions | |

Sheet 4 | Solutions | |

Stage 3 ★★ | Sheet 1 | Solutions |

Sheet 2 | Solutions | |

Sheet 3 | Solutions | |

Stage 4 ★★ | Sheet 1 | Solutions |

Sheet 2 | Solutions | |

Stage 4 ★★★ | Sheet 1 | Solutions |

Age 14 to 16

ShortChallenge Level

Weekly Problem 34 - 2008

What is the area of the region common to this triangle and square?

Age 14 to 16

ShortChallenge Level

Weekly Problem 44 - 2009

A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

Age 14 to 16

ShortChallenge Level

Just from the diagram, can you work out the radius of the smaller circles?

Age 14 to 16

ShortChallenge Level

Weekly Problem 8 - 2010

Are you able to find triangles such that these five statements are true?