"Question 2 Draw the following: A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Practical Geometry Page 68"
Answers
To construct a quadrilateral it is necessary to know at least 5 of its parts.
Measurement of 5 parts of a quadrilateral are sufficient to construct it in the following cases:
1. Four sides and one Diagonal.
2. Three sides and both diagonals.
3. Two adjacent sides and 3 angles.
4. Three sides and two included angles.
5. Four sides and one angle.
It is always convenient and helpful to draw a rough sketch of the quadrilateral and indicate the given measurements.
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[ Figure is in the attachment]
Steps of construction:
(a) Draw a line segment AC = 5.2 cm and draw perpendicular bisectors of AC.
(b) Since, diagonals of rhombus bisect each other at mid-point O, therefore OB=OD = 6.4/2 i.e., 3.2 cm.
(c) Draw two arcs on both sides of AC of radius 3.2 cm from intersection point O, which intersects at B and D.
(d) Join AB, BC, CD and DA.
It is required rhombus ABCD.
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Hope this will help you....
area of a rhombus =1/2 (at1/2 ×5.2 ×(6.4+b)
=166.0