) Construct a Quadrilateral ABCD such that BC = 6.5cm , CD = 4.8cm, A = 80 , B =100 , D =75".
Answers
Step-by-step explanation:
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