# Constructing a quadrilateral when the lengths of four sides and a diagonal are given:

When four sides and a diagonal were given, we first drew a triangle with the available data and then tried to locate the fourth point.

1) Construct a quadrilateral PQRS, where PQ = 4 cm, QR = 6 cm, RS = 5 cm, PS = 5.5 cm and PR = 7 cm.

Step 1: A rough sketch will help us in visualizing the quadrilateral. We draw this first and mark the measurements.

Step 2: From the rough sketch, it is easy to see that ∆PQR can be constructed using SSS construction conditions. Draw ∆PQR.

Step 3: Now, we have to locate the fourth point S. This ‘S’ would be on the side opposite to Q with reference to PR. For that, we have two measurements. S is 5.5 cm away from P. So, with P as center, draw an arc of radius 5.5 cm.

Step 4: S is 5 cm away from R. So with R as the center, draw an arc of radius 5 cm.

Step 5: S should lie on both the arcs drawn. So it is the point of intersection of the two arcs. Mark S and complete PQRS. PQRS is the required quadrilateral.

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Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given [00:07:38]
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