Question

Construct a quadrilateral : ABQP where AB =4 cm,BQ=4.6 cm,QP=5.4cm,AQ=5.8 cm,BP=6.1 cm​

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

Step-by-step explanation: