Question

Construct a quadrilateral ABCD,where AB=4cm,BC=6cm,CD=5cm,AD=5.5cm and AC=7cm.
(i) write the steps of construction.
(ii) How many line segments are there in the figure.Name them.​

Answer 1

Answer:

Given: AB = 4 cm, BC = 6 cm, CD = 5.6 cm, DA = 5 cm and AC = 8 cm.

To construct a quadrilateral

Steps for construction

Step 1 : Draw a rough figure and mark the given measurements.

Step 2 : Draw a line segment AB = 4 cm.

Step 3 : With A and B as centres draw arcs of radii 8 cm and 6 cm respectively and let them cut at C.

Step 4 : Join

AC

and

BC

Step 5 : With A and C as centres draw arcs of radii 5 cm, and 5.6 cm respectively and let them cut at D.

Step 6 : Join

AD

and

CD

. ABCD is the required quadrilateral.

Step 7 : From B draw

BE

⊥

AC

and from D draw

DF

⊥

AC

, then measure the lengths of BE and DF. BE = h

1

= 3 cm and DF = h

2

= 3.5 cm.

AC = d = 8 cm.

Calculation of area:

In the quadrilateral ABCD, d = 8 cm, h

1

= 3 cm and h

2

= 3.5 cm.

Area of the quadrilateral ABCD =

2

1

d(h

1

+h

2

)

=

2

1

(8)(3+3.5)

=

2

1

×8×6.5

=26cm

2

Answer 2

(i) Please refer to the picture for the diagram.

(ii) There are 5 line segments. Namely, AB, AC, DC, BC and DC

GIVEN

Construct a quadrilateral ABCD,where AB=4cm,BC=6cm,CD=5cm,AD=5.5cm and AC

TO FIND

(i) write the steps of construction.

(ii) How many line segments are there in the figure.Name them.

SOLUTION

The above problem can be simply solved as follows;

• Step 1. 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.

ABCD is the required quadrilateral.

(ii) There are 5 line segments. Namely, AB, AC, DC, BC and DC

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