Construct a trapezium BOAT in which BO is parallel to TA, BO=7cm, OA=6cm, BA=10cm and TA=6cm. Also find its area.
Answers
Step-by-step explanation:
ANSWER
Given:
AB
is parallel to
DC
, BC = 5 cm, CD = 4 cm and AD = 5 cm.
Steps for construction:
Step 1 : Draw a rough diagram and mark the given measurements. Draw
CE
∥
DA
. Now AECD is a parallelogram. ∴ EC = 5 cm, AE = DC = 4 cm, EB = 3cm.
Step 2 : Draw a line segment AB = 7 cm.
Step 3 : Mark E on
AB
such that AE = 4 cm . [ ∵ DC = 4 cm ]
Step 4 : With B and E as centres draw two arcs of radius 5 cm and let them cut at C.
Step 5 : With B as centre and radius 6 cm draw an arc cutting
BY
at C.
Step 6 : With C and A as centres and with 4 cm and 5 cm as radii draw two arcs. Let them cut at D.
Step 7 : Join
AD
and
CD
. ABCD is the required trapezium.
Step 8 : From D draw
DF
⊥
AB
and measure the length of DF. DF = h = 4.8 cm, AB = a = 7 cm, CD = b = 4 cm.
Calculation of area:In the trapezium ABCD, a = 7 cm, b = 4 cm and h = 4.8 cm.
Area of the trapezium ABCD =
2
1
h(a+b)
=
2
1
(4.8)(7+4)
=
2
1
× 4.8 × 11
= × 2.4 × 11
=26.4 cm
2
Answer:
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