Construct a quadrilateral ABCD such that angle BAD = 60°, BC = 7cm and AB = 10cm. Measure and write down the length of CD. Bisect the quadrilateral ABCD, draw the locus of points which are equidistant from BC and CD.

Draw a line segment AB of length 10 cm.

At point A, use a protractor to draw a line segment AD such that $\angle BAD = 60^\circ$.

Measure 8 cm along the line segment AD from point A and mark point D.

At point B, use a protractor to draw a line segment BC such that $\angle ABC = 120^\circ$.

Measure 7 cm along the line segment BC from point B and mark point C.

Join points C and D to complete the quadrilateral ABCD.

Part b): Measure the length of CD

Using a ruler, measure the length of the line segment CD that you constructed in Part a).

The length of CD will depend on the accuracy of your construction. For example, it might be around 7.5 cm to 8.5 cm.

Part c): Drawing Loci

c)i) Locus of points 8 cm from A.

With A as the center and a radius of 8 cm, draw an arc. This arc represents all points 8 cm from A. Only consider the portion of the arc that lies within the quadrilateral ABCD.

c)ii) Locus of points equidistant from BC and CD.

The locus of points equidistant from two intersecting lines (or line segments) is the angle bisector of the angle formed by those lines. In this case, you need to bisect $\angle BCD$.

Draw the angle bisector of $\angle BCD$. Only consider the portion of the bisector that lies within the quadrilateral ABCD.

Part d): Labeling point P

Point P is the intersection of the locus from c)i) (arc 8 cm from A) and the locus from c)ii) (angle bisector of $\angle BCD$) within the quadrilateral ABCD.

Mark this intersection point as P.

Part e): Shading the region for Q

Point Q is within the quadrilateral ABCD such that:

1. It is nearer to CD than BC.
2. It is greater than or equal to 3 cm from A.

This region is on the side of the angle bisector of $\angle BCD$ (drawn in c)ii)) that is closer to CD.

Draw an arc with A as the center and a radius of 3 cm. The region "greater than or equal to 3 cm from A" is outside this arc (further away from A).

The region for Q is the area within the quadrilateral ABCD that satisfies both conditions: it is on the side of the angle bisector closer to CD, AND it is outside or on the arc of radius 3 cm from A. Shade this specific region.

Since I cannot perform the physical construction, I cannot provide numerical answers for parts b) and d) or an image for part e). However, these steps guide you through the process.