Construct a trapezium ABCD where AB || CD and also AB= 7 cm,
BC=5 cm, CD = 3 cm and ∠ C = 110o
. (Hint: using AB || CD , find ∠B
Answers
Answer:Given:
AB
is parallel to
DC
, BC = 6 cm, ∠ BAD = 80
o
and ∠ ABC = 70
o
.
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 7 cm.
Step 3 : On
AB
at A make ∠ BAX measuring 80
o
.
Step 4 : On
AB
at B make ∠ ABY measuring 70
o
.
Step 5 : With B as centre and radius 6 cm draw an arc cutting
BY
at C.
Step 6 : Draw
CZ
parallel to
AB
. This cuts
AX
at D. ABCD is the required trapezium.
Step 8 : From C draw
CE
⊥
AB
and measure the length of CE. CE = h = 5.6 cm, CD = b = 4 cm Also AB = a = 7 cm.
Calculation of area:
In the trapezium PQRS, a = 7 cm, b = 4 cm and h = 5.6 cm.
Area of the trapezium ABCD =
2
1
h(a+b)
=
2
1
(5.6)(7+4)
=
2
1
× 5.6 × 11
=30.8 cm
2
Step-by-step explanation: