Question

ABCD is a trapezium, where AB is parallel to DC . If AB = 4cm, BC =3cm, CD = 7 cm and DA = 2 cm, then what is the area of the trapezium ?
(a) 22√2/3 cm²
(b) 22√3/2cm²
(c) 22√3 cm²
(d) 22√2/3cm²

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Answer 1

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