Question

8. In the given figure, ABCD is a rectangle in which AB = 60 cm and BC = 40 cm. If P, Q, R and S be thé mid-points of AD, DC, CB and BA, find the area of the shaded region. Ans 1200 cm sq​

Answer 1

Answer:

given

ab=60cm

bc=40cm

p,q,r,s are the midpoints

to find

area of shaded region

solution:

AS=SB= 30cm

BR=CR= 20cm

 join p and r, q and s

in triangle QOR

base=OR=30cm

height= OQ= 20cm

area of triangle QOR=

1/2 ×B×H

1/2×30×20

= 300cm^2

area of the shaded region = 300×4

=1200cm^2

Answer 2

Answer:

area of the rectangle ABCD is 60cm×40cm

=2400 sq cm

In the figure,

P is the midpoint of AD

so,AP=40/2 cm=20cm=PD

similarly, BR=RC=20cm

again Q is the midpoint of DC

so,DQ=QC=60/2 cm=30 cm

area of the triangle PDQ,

1/2.DQ.PD sq cm

=30×20/2 sq cm=300 sq cm

similarly,triangle RCQ=300sq cm

triangle SBR=300sq cm

triangle APS÷300sq cm

area of the shaded region is

(2400-4.300)sq cm

=(2400-1200) sq cm

=1200sq cm