Core stretch Twelve identical isosceles triangles, each with base $x$ cm and equal sides $y$ cm,

Question

Core stretch

Twelve identical isosceles triangles, each with base $x$ cm and equal sides $y$ cm, tessellate the trapezium shown. The outer boundary consists of six $x$-segments and four $y$-segments, while the complete wire network contains nine $x$-segments and fourteen $y$-segments. The outer perimeter is $54$ cm and the total wire length is $126$ cm.

Form two equations and find $x,y$.[2]
Hence find the trapezium area.[2]

Accepted Answer

(a) $6x+4y=54,\ 9x+14y=126$; $x=5.25\text{ cm},\ y=5.625\text{ cm}$. (b) $47.25\sqrt{11}=156.7\text{ cm}^2$ (1 d.p.).

Wire tessellation of an isosceles-triangle trapezium

Wire tessellation of an isosceles-triangle trapezium

Solution:

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