11 Plus Exams Forum

Four of these shapes will fit together with shapes of the same kind, without leaving any gaps.

There are 5 pictures.

I am not sure how to do this

Thanks for your help.

I suspect that I would expect a 10 year old to do this by examining the shapes and using trial and error to be honest. But mathemaxztically the explanations would go along these lines:

Angles around a point must add up to 360.

Shape A (equiliateral triangle) has internal angles of 60. 6 x60 = 360. so you can put 6 triangles together around a single point with no gap.
Shape B is also a triangle, this time scalene. Here the angles all add up to 180. Again therefreo is is possible to arrange 6 of these triangles around a single point.
Shape C (rectangle) has internal angles of 90. 4 x 90 = 360. So you can put 4 rectangles around a single point with no gap.
Shape D (regular pentagon). The external angles of a pentagon are 360/5=72 so internal angles are 108. 360 is not exactly divisible by 108 so you cannot fit the pentagons around a single point without a gap.
Shape E (regular hexagon) has external angles of 360/6 = 60 so internal angles of 120. 360/120=3 so you can fit 3 hexagons around a single point with no gap.