Construction of Polygons

• Construction of quadrilateral when one angle and four sides are given:

Example:

Construct a quadrilateral PQRS with PQ = 6 cm, QR = 7 cm, RS = 8.5 cm, PS = 6.5 cm and ∠Q = 90°.

Solution:

Step 1: Draw line segment PQ of length 6 cm.

Step 2: Draw ∠XQP = 90° at point Q.

Step 3: Taking Q as centre and 7 cm as radius, mark an arc on QX and name the point of intersection as R.

Step 4: Taking R as centre and 8.5 cm as radius, mark an arc.

Step 5: Taking P as centre and 6.5 cm as radius, mark an arc. Let it intersect the previous arc at point S.

Step 6: Join PS and RS.

PQRS is the required quadrilateral.

• Construction of a quadrilateral when three sides and two included angles are given

Example:

Construct a quadrilateral PQRS with SR = 6.5 cm, PS = 5 cm, QR = 3 cm, ∠R = 120°, and ∠S = 70°.

Solution:

The steps of construction are as follows:

Step 1:

Draw SR = 6.5 cm. Draw ∠SRX = 120° at R and ∠RSY = 70° at S.

Step 2:

With S as centre, draw an arc of radius 5 cm intersecting SY at P.

With R as cen…