(vi) AC = 6.5 cm, AB = 6.5 cm, = angle CAB 105 degree
Answers
Answer:
Answer
Given:
AB = 6.5 cm, AD = 5 cm, CD = 5 cm, ∠ BAC = 40
o
and ∠ ABC = 50
o
.
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 6.5cm.
Step 3 : At A on
AB
make ∠BAX whose measure is 40
0
and at B on
AB
make ∠ABY whose measure is 50
0
. They meet at C.
Step 4 : With A and C as centres draw two arcs of radius 5cm and let them cut at D.
Step 5 : Join
AD
and
CD
. ABCD is the required quadrilateral.
Step 6 : From D draw
DE
⊥
AC
and from B draw
BC
⊥
AC
. Then measure the lengths of BC and DE. BC = h
1
= 4.2 cm, DE = h
2
= 4.3 cm and AC = d = 5 cm.
Calculation of area:
In the quadrilateral ABCD, d = 5 cm, h
1
= 4.2 cm and h
2
= 4.3 cm.
Area of the quadrilateral ABCD =
2
1
d(h
1
+h
2
)
=
2
1
(57.8)(4.2+4.3)
=
2
1
×5×8.5
=21.25 cm
2