Constructing Quadrilateral GOLD:

To construct the quadrilateral GOLD, we will follow the given instructions and use basic geometric construction techniques. Let's break down the steps involved:

Step 1: Draw Line Segments:
- Take a blank sheet of paper and draw a line segment OL of length 7.5 cm.
- Mark point O as the starting point of the line segment.
- Measure and mark a point L on the line segment OL, such that OL = 7.5 cm.

Step 2: Construct Point G:
- Using a compass, set the width to 6 cm.
- Place the compass at point O and draw an arc that intersects the line segment OL at two points, labeled as A and B.
- Without changing the compass width, place the compass at point L and draw another arc that intersects the line segment OL at two points, labeled as C and D.
- Draw a straight line through points A and C, and label their intersection as point G.
- Measure and ensure that the distance between points O and G is equal to 6 cm.

Step 3: Construct Point D:
- Using a compass, set the width to 6 cm.
- Place the compass at point G and draw an arc that intersects the line segment OL at two points, labeled as E and F.
- Without changing the compass width, place the compass at point L and draw another arc that intersects the line segment OL at two points, labeled as H and I.
- Draw a straight line through points E and H, and label their intersection as point D.
- Measure and ensure that the distance between points G and D is equal to 6 cm.

Step 4: Construct Point O:
- Using a compass, set the width to 10 cm.
- Place the compass at point D and draw an arc that intersects the line segment OL at two points, labeled as J and K.
- Without changing the compass width, place the compass at point G and draw another arc that intersects the line segment OL at two points, labeled as M and N.
- Draw a straight line through points J and M, and label their intersection as point O.
- Measure and ensure that the distance between points D and O is equal to 10 cm.

Step 5: Complete the Quadrilateral:
- Connect points O, L, and D to form a triangle.
- Connect points O and G, and points G and D to complete the quadrilateral.

Important Measurements:
- OL = 7.5 cm
- GL = 6 cm
- GD = 6 cm
- LD = 5 cm
- OD = 10 cm

Note: The above steps and measurements are given for demonstration purposes. Please refer to the provided instructions and adjust the measurements accordingly while constructing the quadrilateral GOLD.