Theory:

  • Depending upon the lengths of the sides and diagonal, create a triangle of \(PQR\) based on \(SSS\) construction.
      7.PNG
  • Make an arc (point \(S\)) at a certain distance from \(P\).
      6.PNG
  • Make an arc at a certain distance from point \(R\) on the earlier arc on \(S\). Name the two points intersection as \(S\).
      5.PNG
  • \(P\) and \(R\) join \(S\). The quadrilateral \(PQRS\) will be achieved.
       4.PNG
Example:
Construct a quadrilateral \(ABCD\) with the following measurements.
 
\(AB =\) \(4.5 cm\), \(BC =\) \(5.5 cm\), \(CD = 4cm\), \(AD = 6cm\), \(AC = 7cm\).
 
Step 1:Draw side \(BC = 5.5 cm\) and cut arcs above it from \(B\) (\(4.5 cm\)) and \(C\) (\(7 cm\)). Mark the intersection as \(A\). Join \(AB\) and \(AC\).
 
3.PNG
 
Step 2: Draw and arc from \(A\) equal to \(6 cm\) which is the length of \(AD\).
 
2.PNG
 
Step 3: Draw and arc from \(C\) equal to \(4 cm\) which is the length of \(CD\). Mark the intersection as \(D\) and join \(AD\) and \(CD\).
 
1.PNG
 
Thus, the \(ABCD\) is a required quadrilateral.
 
Calculate Area of quadrilateral:

Area of the quadrilateral \(ABCD\) \(=\) \(\frac {1}{2}\) \(\times\) d \(\times\) \(h_1 + h_2\) sq. units
 
\(=\) \(\frac{1}{2} × 10 (1.9 +2.3)\)
 
\(=\) \(5\times 4.2\)
 
\(=\) \(21 cm²\).