﻿ Construct a quadrilateral ABCD when AB = 4 cm, BC = 6 cm, CD = 5 cm, AD = 5.5 cm and AC = 7 cm. from Mathematics Practical Geometry Class 8 Manipur Board

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# Construct a quadrilateral ABCD when AB = 4 cm, BC = 6 cm, CD = 5 cm, AD = 5.5 cm and AC = 7 cm.

First of all make a rough sketch. Do not start construction without drawing a rough sketch showing sides, angles and diagonals, etc., with correct name.
Step I. Draw a rough sketch and mark the measurements.
Step II. Draw AC = 7 cm.
Step III. With A as centre and radius 4 cm, draw an arc above AC.
Step IV. With C as centre and radius 6 cm, draw another arc intersecting the previous arc at B.
Step V. With centre A and radius 5.5 cm, draw an arc below AC.
Step VI. With centre C and radius 5 cm, draw another arc to intersect the previous arc at D.
Step VII. Join DA and DC.

Thus, ABCD is the required quadrilateral.

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Draw a rectangle PQRS in which PQ = 7.2 cm and QR = 5.4 cm.

Steps of construction:
I.       Draw a line segment PQ = 7.2 cm.
II.      At P,    draw  such that
III.    From PX, cut off PS = 5.4 cm.
IV.    At Q, draw  such that .
V.     From QY, cut off QR = 5.4 cm.
VI.    Join R and S.
Thus, PQRS is the required rectangle.

364 Views

Draw a rhombus ABCD such that BD = 5.6 cm and AC = 6.6 cm.

Steps of construction:
I.    Draw a line segment AC = 6.6 cm.
II.   Draw perpendicular bisector XY of AC, which meets AC at M.
III.  With centre M and radius  =
i.e.  2.8 cm, draw arcs to intersect XY at B and D.
IV.  Join AB, BC, CD and AD.
Thus, ABCD is the required rhombus.

943 Views

Construct a quadrilateral ABCD such that AB = 4.5 cm, BC = 3.2 cm, CD = 5 cm, DA - 2.6 cm and BD = 4.5 cm.

Steps of construction:
I. Draw a line AB = 4.5 cm.
II. With centre A and radius = 2.6 cm, draw an arc.
III. With centre B and radius = 4.5 cm, draw another arc such that it intersects the previous arc at D.
IV. With centre D and radius = 5 cm, draw an arc.
V. Again with centre B and radius = 3.2 cm, draw another arc to intersect the previous arc at C.
VI. Join AD, BC and DC.
Thus, ABCD is the required quadrilateral.

225 Views

Draw a quadrilateral in which AB = 4.5 cm, BC = 5.1 cm, CD = 3.9 cm, ∠B = 90° and ∠C = 120°.

Steps of construction:
I.      Draw a line segment AB = 4.5 cm.
II.     At B, construct
III.    From  cut off BC = 5.1 cm.
IV.    AT C, draw  such that
V.     From  cut off CD = 3.9 cm.