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Shapely Pairs

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
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You're going to have to come up with a system to make sure that you don't miss out any pairs, and to make sure that you don't count any twice. You could pick one card and see how many other cards could be paired with it, to get you started.

Is it possible to pair all the cards? Try playing around with different possibilities. You might have to pair up some cards first, if they don't have many possible partners.

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Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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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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