construct a quadrilateral ABCD in which AB =4.1 cm , BC =3.6 cm CD=6.1 cm , DA =5.1 cm and \ABC =120°
Answers
Answer:
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