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Home >> Quadrilateral >> Construction of Quadrilateral (compass) >> Construction of Quadrilateral where four sides & one diagonal are given >>

Construction of Quadrilateral where four sides & one diagonal are given

Construction of Quadrilateral where four sides & one diagonal are given Construction of Quadrilateral where three sides & two diagonals are given Construction of Quadrilateral where two adjacent sides and three angles are given Construction of Quadrilateral where three sides and two included angles are given

Construct a quadrilateral ABCD, where sides AB = 7 cm, BC = 8 cm, CD = 6 cm, & DA = 5 cm and diagonal BD = 10 cm

Solution: As per the given question:
AB, BC, CD, DA are the four sides of quadrilateral ABCD.
And BD is one of diagonal.

Steps of construction are as follows:

Step 1: Use ruler and draw a line segment of 10 cm. Name this line segment as BD and this will be the diagonal of quadrilateral ABCD (as shown below):



Step 2: Use compass and 7 cm wide open. With B as center, draw an arc (as shown below):



Step 3: Again use compass and 5 cm wide open. With D as center, draw an arc which cuts previous arc (made in step 2), (as shown below):



Step 4: Mark point of intersection of both arcs as Point A (as shown below):



Step 5 : Use ruler and join points B & A and points D & A (as shown below)



Step 6: Use ruler and measure the length of AB and DA. On measuring, you should get AB = 7 cm and DA = 5 cm (you can here notice that the measurement of AB and DA is similar to as given in the question). And we get:



Step 7: Now, again use compass and 8 cm wide open. With B as center, draw an arc (as shown below):



Step 8 : Again use compass and 6 cm wide open. With D as center, draw another arc which cuts previous arc (made in step 7), (as shown below):



Step 9: Mark point of intersection of both arcs as Point C (as shown below):



Step 10: Use ruler and join points B & C and points C & D (as shown below)



Step 11: Use ruler and measure the length of BC and CD. On measuring, you should get BC= 8 cm and CD = 6 cm (you can here notice that the measurement of BC and CD is similar to as given in the question). And we get resultant quadrilateral ABCD:


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