Construction of Quadrilateral ABCD

To construct a quadrilateral ABCD, we are given the following information:
- AB = 4.2 cm
- BC = 4.5 cm
- CD = 4 cm
- OA = 4.8 cm
- ∠A = 72°

Now, let's proceed with the construction step by step:

Step 1: Draw a line segment AB
- Take a ruler and draw a line segment AB of length 4.2 cm. Label the endpoints as A and B.

Step 2: Construct angle A
- Using a protractor, measure an angle of 72° at point A. Make sure the arms of the angle extend beyond line segment AB.

Step 3: Construct a line perpendicular to AB at point A
- Place the compass at point A and draw an arc that intersects both arms of angle A. Label the points of intersection as C and D.

Step 4: Draw line segments AC and AD
- Using a ruler, draw line segments AC and AD to connect points A to C and A to D, respectively.

Step 5: Construct a line perpendicular to BC at point C
- Place the compass at point C and draw an arc that intersects line segment BC. Label the point of intersection as F.

Step 6: Construct a line perpendicular to CD at point C
- Place the compass at point C and draw an arc that intersects line segment CD. Label the point of intersection as E.

Step 7: Draw line segments CE and CF
- Using a ruler, draw line segments CE and CF to connect points C to E and C to F, respectively.

Step 8: Draw line segments BD and EF
- Using a ruler, draw line segments BD and EF to connect points B to D and E to F, respectively.

Step 9: Label the vertices and sides
- Label the vertices of the quadrilateral as A, B, C, and D in clockwise order.
- Label the sides of the quadrilateral as AB, BC, CD, and DA.

Now, the quadrilateral ABCD is constructed with the given specifications:
- AB = 4.2 cm
- BC = 4.5 cm
- CD = 4 cm
- OA = 4.8 cm
- ∠A = 72°

Please note that the angles and lengths mentioned in the construction may not be perfectly accurate due to the limitations of the drawing tools.

It's not possible to construct this quadrilateral in this app