# Four Sides and One Diagonal

Construct a quadrilateral ABCD given that = 5cm, = 3cm, = 5cm and = 4cm and diagonal = 6cm

Steps :

**(a)** Draw a line segment =5cm

**(b)** With A and B as centres, and 6cm and 3cm as radii respectively, draw arcs to cut each other at C.

**(c)** Join AC and BC

**(d)** Now with A and C as centres and 4cm and 5cm as radii respectively draw two arcs to cut each other at D.

**(e)** Join AD and CD. ABCD is the required Quadrilateral.

constructing Î”ADC |

constructing Î”ABC |

To construct a quadrilateral given four sides and a diagonal (SSSSD case)

Let the given measures be AB = 4.5 cm, BC = 5.6 cm, CD = 5.9 cm, DA = 5.2 cm and diagonal AC = 6.8 cm.

The two triangles we can construct to complete the quadrilateral are DADC and DABC.

**(a)** Constructing DADC

1. Draw DC = 5.9 cm.

2. With C as centre and radius 6.8 cm, draw an arc.

3. With D as centre and radius 5.2 cm, draw another are to cut the previous arc at A.

4. Join CA, and DA

**(b)** Constructing DABC

5. With C as centre and radius 5.6 cm, draw an arc on the other side of AC.

6. With A as centre and radius 4.5 cm, draw another arc to cut the previous arc at B.

7. Join CB and AB.