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Areas of Parallelograms

Age 14 to 16
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
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Try drawing a rectangle around the parallelogram. If you can work out the area of the rectangle and the areas of the parts of the rectangle outside the parallelogram, then you should be able to find the area of the parallelogram.

Don't forget that you can break up complicated shapes into simpler small shapes (such as triangles and rectangles) whose areas are easier to find.

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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Equilateral Areas

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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