Construction of Quadrilateral when the length of four sides and a diagonal are given
Construction of Quadrilateral when the length of four sides and a diagonal are given
Construction of Quadrilateral when the length of Four Sides and one diagonal are given: A quadrilateral can be constructed when four sides and a diagonal is given to us.We will follow the steps given below to construct such type of quadrilateral.:
| Step 1 Draw a line segment equal to the length of one daigonal for example BD. |  |
Step 2 With B as centre and radius equal to the length given for BA, draw an arc. |  |
| Step 3 With D as centre and radius equal to the length given for AD draw an arc intersecting the arc drawn in step 2 and mark the point of intersection as A |  |
| Step 4 With B as centre and radius equal to the length given for BC draw an arc on the other side of BD as compared to point A. |  |
| Step 5 With D as centre and radius equal to the length given for CD, draw an arc intersecting the arc drawn in step 4 and mark the point of intersection as C |  |
| Step 6 Join BA, DA, BC and CD.. The quadrilateral ABCD so obtained is the required quadrilateral. |  |
Illustration: Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4cm, CD = 6.4 cm, DA = 2.8 cm and BD = 6.6 cm.
Solution First we draw a rough sketch of the quadrilateral ABCD and write down its dimensions along the sides.
We may divide the quadrilateral ABCD into two constructible triangles ABD and BCD. Steps of construction are:
Step 1 Draw BD = 6.6 cm. Step 2 With B as centre and radius BC = 4 cm, draw an arc. Step 3 With D as centre and radius CD = 6.4 cm, draw an arc intersecting the arc drawn in step 2 and mark the point of intersection as C. Step 4 With B as centre and radius BA = 4.4 cm, draw an arc on the other side of BD as compared to point C. Step 5 With D as centre and radius AD = 2.8 cm, draw an arc intersecting the arc drawn in step 4 and mark the point of intersection as A Step 6 Join BA, DA, BC and CD. |  |
The quadrilateral ABCD so obtained is the required quadrilateral.
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