Question

6. In the given
figure, ABCD is
a trapezium in
which AB = 18 cm
and CD = 10 cm.
The area of AACD A
is 75 cm. Find the
area of ABCD.
B
18​

Answer 1

Answer:

Given-

ABCD is a trapezium. AB∥DC and AB=18 cm, DC=32 cm.

There are 4 arcs centring the vertices A,B,C,D with radius r=7 cm.

To find out - area of shaded region

Solution-

Area of trapezium =

2

1

× sum of the parallel sides × distance between the parallel sides.=

2

1

×(AB+CD)×14=

2

1

×(18+32)×14cm

2

=350 cm

2

.

Let us take the angles of the trapezium as a at A,b at B,c at C and d at D.

Now the given arcs form 4 sectors.

Together they form a circle of radius r=7 cm as a+b+c+d=360

o

.

∴ The area of the sectors=area of circle with radius (r=7cm) =π×r

2

=

7

22

×7

2

=154 cm

2

.

∴ Area of shaded region = area of trapezium − area of circle

=(350−154)=196 cm

2

.