Question

2. Construct a quadrilateral ABCD with the following measurements.
AB = 6 cm, BC = 6.5 cm, CD = 4.5 cm, DA = 4.5 cm, BD = 6.8 cm
​

Answer 1

Step-by-step explanation:

Given:

AB = 6 cm, BC = 4 cm, CD = 5 cm, DA = 4.5 cm ∠ ABC = 100

o

.

Steps for construction

Step 1 : Draw a rough diagram and mark the given measurments.

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

Step 3 : At B on

BC

make ∠ CBX whose measure is 100

o

.

Step 4 : With B as centre and radius 6 cm draw an arc. This cuts

BX

at A. Join

CA

Step 5 : With C and A as centres, draw arcs of radii 5 cm and 4.5 cm respectively and let them cut at D.

Step 6 : Join

CD

and

AD

. ABCD is the required quadrilateral.

Step 7 : From B draw

BF

⊥

AC

and from D draw

DE

⊥

AC

. Measure the lengths of BF and DE. BF = h

1

= 3 cm, DE = h

2

= 2.7 cm and AC = d = 7.8 cm.

Calculation of area:

In the quadrilateral ABCD, d = 7.8 cm, h

1

= 3 cm and h

2

= 2.7 cm.

Area of the quadrilateral ABCD =

2

1

d(h

1

+h

2

)

=

2

1

(7.8)(3+2.7)

=

2

1

×7.8×5.7

=22.23 cm

2