Question

Construct the following quadrilaterals.
(i) Quadrilateral ABCD
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm
(ii) Parallelogram MORE
OR = 6 cm
RE = 4.5 cm
EO = 7.5 cm
(iii) Rhombus BEST
BE = 4.5 cm
ET = 6 cm

Answer 1

Hint: First draw one given line in each of the following quadrilaterals and then go step by step from the given dimensions and draw arc using compass for the given lengths of the sides of the quadrilaterals.

Complete step-by-step answer:
(i)
Step 1: - Draw the line AB of length 4.5 cm

Step 2: - Place a compass on point B and draw an arc of radius 5.5 cm taking B as the centre.

Step 3: - Now draw another arc with centre at point A and radius 7 cm which meets the previous arc at point C.

Step 4: - Draw an arc of radius 6cm from point A as centre.

Step 5: - Now draw an arc of radius 4 cm from point C as centre which meets the former arc at point D.

Step 6: - Now join the points BC, CD and AD. And ABCD will be the required quadrilateral.

(ii)
Step 1: - Draw the line OR of length 6 cm

Step 2: - Place a compass on point R and draw an arc of radius 4.5 cm taking R as the centre.

Step 3: - Now draw another arc with centre at point O and radius 7.5 cm which meets the previous arc at E.

Step 4: - Draw an arc of radius 4.5 cm from point O as centre.

Step 5: - Now draw an arc of radius 6 cm from point E as centre which meets the former arc at point M.

Step 6: - Now join the points OM, RE and EM. And MORE will be the required quadrilateral.

(iii)
Step 1: - Draw the line BE of length 4.5 cm

Step 2: - Place a compass on point B and draw an arc of radius 4.5 cm taking B as the centre.

Step 3: - Now draw another arc with centre at point E and radius 6 cm which meets the previous arc at T.

Step 4: - Draw an arc of radius 4.5 cm from point E as centre.

Step 5: - Now draw an arc of radius 4.5 cm from point T as centre which meets the former arc at point S.

Step 6: - Now join the points BT, ES and TS. And BEST will be the required quadrilateral.

Note:Whenever we come up with this type of problem then while doing construction we should take in mind the type of quadrilateral given because that will help us in solving problem like if the quadrilateral is given as rhombus and length of its only one side is given then we can draw that rhombus using the property that all sides of the rhombus are equal. And if the quadrilateral is given as a parallelogram then all its sides must be parallel.