Q. 24.5( 20 Votes )

# Construct quadrilaterals for measurements given below:

A rhombus SOAP with SA = 4.3 cm, OP = 5 cm

Answer :

**GIVEN :** In rhombus SOAP,

SA = 4.3 cm

OP = 5 cm (diagonals)

**PROCEDURE** :

**Step 1** : Draw a rough sketch of rhombus SOAP and mark th given measurements.

The diagonals of a rhombus bisect each other perpendicularly.

SA and OP are diagonals of the rhombus SOAP which bisect each other at ‘B ie. ∠ SBO = 90° and OB = BP = = = 2.5cm.

**Step 2** : Draw SA = 4.3cm (one diagonal of the rhombus SOAP) and draw a perpendicular bisector XY of it and mark the point of intersection as ‘B’.

**Step 3** : As the other diagonal OP is perpendicular to SA , OP is a part of XY. So, with center ‘B’ and radius 2.5 cm (OB = BP = 2.5cm) draw 2 arcs on either sides of SA to cut XY at O and P.

**Step 4** : Join S,O ;O,A ; A,P ; S,P to complete the required rhombus SOAP.

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