Question

Construct a rhombus PAIR given that PA=6 cm and angle A=110°

Answer 1

Since the side of the rhombus is 6 cm and one angle = 110deg, it can be constructed easily . Actually two equilateral triangles on the same base will result in the rhombus.

Draw a line PA, 6 cm long.

With A as centre and a radius of 6 cm draw arcs above and below the line PA.

With P as centre and the same radius of 6 cm draw arcs above and below the line PA to cut the arcs drawn earlier. Let the intersections be I and R. Join PI ,lA ,and AR and you have the desired rhombus. <PAI = <ARP = 110 deg, while <IPR = <IAR = 220deg.

Answer 2

Given : PA = 6 cm and angle ∠A = 110°

To Find : construct the rhombus PAIR

Solution:

Step 1 : Draw a line segment PA  = 6 cm

Step 2 : Draw an angle of 110° at A on PA using protractor

Step 3 : Take  a length of  6 cm from A on angle drawn and mark as I

Step 4 : Using compass width = 6 cm and taking I as center draw an arc

Step 5 : Keeping compass width = 6 cm and taking P as center draw an arc such that it intersects arc drawn in previous step at  R

Step 6 : Join IR and PR

Rhombus PAIR is constructed

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