Using a ruler and a pair of compass only construct a trapezium ABCD in which AB =5cm AD=6cm DC =10cm, angle BAD=105 degrees and AB is parallel to DC. Draw a perpendicular from B to DC hence measure the height of the trapezium

Mathematics

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Here are the steps to construct the trapezium and measure its height:

  1. Draw a line segment AB of length 5 cm.

  2. Construct an angle of 105∘105^\circ at point A.

    • Place the compass at A and draw an arc that intersects AB (let's call the intersection point P).
    • With the same radius, place the compass at P and draw an arc (Q). Then, from Q, draw another arc (R). These mark 60∘60^\circ and 120∘120^\circ.
    • Bisect the angle between Q and R to construct a 90∘90^\circ line.
    • Bisect the angle between the $90
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