Construction Of Quadrilaterals is easy if you have a complete grip on the concept. A quadrilateral is a polygon with 4 sides, 4 angles, and also 4 vertices. When you add the interior angles of a quadrilateral, then you can get 360 degrees. The quadrilateral side lengths and angles may different. Depending on the lengths and angles of the sides, you can easily know what is the name of the quadrilateral. You can easily construct a quadrilateral by considering the following criteria.
(i) 4 sides and 1 diagonal is given.
(ii) 3 sides and including 2 angles are given
(iii) 2 sides and three angles are given
(iv) 3 sided and 2 diagonals are given
(v) 4 sides and 1 angle is given
1. Construct the Quadrilateral when 4 sides and 1 diagonal is given
PQ = 5 cm
QR = 4.5 cm
RS = 3.8 cm
PS = 4.4 cm
Diagonal PQ = 6 cm
Steps of Construction:
Firstly, draw a rough figure of the quadrilateral with the given dimensions.
1. Draw a line segment of length 5 cm and mark the ends as P and Q.
2. Take the point P as a center and draw an arc by taking the radius 6 cm.
3. Next, take point Q as a center and draw an arc by taking the radius 4.5 cm. Mark the point as R where the two arcs cross each other. Join the points Q and R as well as P and R.
4. By taking the point P as a center, draw an arc with a radius of 4.4 cm.
5. By taking the point R as a center, draw an arc with a radius of 3.8 cm.
6. Mark the point as S where the two arcs cross each other. Join the points R and S as well as P and S.
The final result is the required quadrilateral.
2. Construct the Quadrilateral when 3 sides and including 2 angles are given
PQ = 3.8 cm
QR = 4.2 cm
PS = 5.2 cm
∠QPS = 180º
∠PQR = 80º
Steps of Construction:
Firstly, draw a rough figure of the quadrilateral with the given dimensions.
1. Draw a line segment of length 3.8 cm and mark the ends as P and Q.
2. Take point P as a center and make a point by taking 180º using a protector.
3. Next, take point P as a center and draw an arc by taking the radius 5.2 cm. Mark the point as S where the point and arc cross each other. Join the points P and S.
4. By taking the point Q as a center, make a point by taking 80º using a protector.
5. By taking the point Q as a center, draw an arc with a radius of 4.2 cm.
6. Mark the point as R where the point and arc cross each other. Join the points Q and R.
7. Finally, join the points R and S and draw a line segment.
The final result is the required quadrilateral.
3. Construct the Quadrilateral when 3 sides and including 2 angles are given
AB = 4.7 cm
∠ABC = 120°,
BC = 4 cm,
∠BCD = 100°, and ∠BAD = 60°.
Steps of Construction:
Firstly, draw a rough figure of the quadrilateral with the given dimensions.
1. Draw a line segment of length 4.7 cm and mark the ends as A and B.
2. Take point A as a center and make a point by taking 60º using a protector.
3. Next, take point B as a center and make a point by taking 120º using a protector. Mark the point as D where the two points are meet at a point. Join the points A and D.
4. By taking the point B as a center, draw an arc with a radius of 4 cm.
5. Mark the point as C where the point and arc cross each other. Join the points B and C.
6. Finally, join the points C and D and draw a line segment.
The final result is the required quadrilateral.
4. Construct the Quadrilateral when 3 sided and 2 diagonals are given
PQ = 4.2 cm
QR = 4 cm
PS = 3.2 cm
Diagonal PR = 5 cm
Diagonal QS = 4.6 cm
Steps of Construction:
Firstly, draw a rough figure of the quadrilateral with the given dimensions.
1. Draw a line segment of length 4.2 cm and mark the ends as P and Q.
2. Take the point P as a center and draw an arc by taking the radius 5 cm.
3. Next, take point Q as a center and draw an arc by taking the radius 4 cm. Mark the point as R where the two arcs cross each other. Join the points Q and R as well as P and R.
4. By taking the point P as a center, draw an arc with a radius of 3.2 cm.
5. By taking the point Q as a center, draw an arc with a radius of 4.6 cm.
6. Mark the point as S where the two arcs cross each other. Join the points R and S as well as P and S.
The final result is the required quadrilateral.
5. Construct the Quadrilateral when 4 sides and 1 angle is given.
PQ = 4 cm, QR = 3.6 cm, RS = 4.7 cm, PS = 5.2 cm and ∠B = 80°.
Steps of Construction:
Firstly, draw a rough figure of the quadrilateral with the given dimensions.
1. Draw a line segment of length 4 cm and mark the ends as P and Q.
2. Take point Q as a center and make a point by taking 80º using a protector.
3. Next, take point Q as a center and draw an arc with a radius of 3.6 cm. Mark the point as R where the two points are meet at a point. Join the points Q and R.
4. By taking the point P as a center, draw an arc with a radius of 5.2 cm.
5. By taking the point R as a center, draw an arc with a radius of 4.7 cm.
6. Mark the point as S where the two arcs cross each other. Join the points P and S, R and S.
The final result is the required quadrilateral.
