constructed a quadrilateral abcd with ab=6.5cm,bc=7cm , cd=5cm, ad=6cm and ac=5.5cm
Answers
Answer:
AB = 6.5 cm, AD = 5 cm, CD = 5 cm, ∠BAC = 40
∘
and ∠ABC = 50
∘
.
Steps for construction:
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB=6.5 cm.
Step 3 : At A on
AB
make ∠BAXwhose measure is 40
∘
and at B on
AB
make ∠ABYwhose measure is 50
∘
. They meet at C.
Step 4 : With A and C as centres draw two arcs of radius 5 cm 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
=21.25cm
2