Question

ABCD is a rectangle
having length 40 cm
and breadth 26 cm.
P, Q, R, and S are the
midpoints of AB, BC,
CD and AD
respectively. If BD is
the diagonal, what is
the area (in cm) of
the shaded
part?
AT
R​

Answer 1

Step-by-step explanation:

Given that:

ABCD is a rectangle having length 40 cm and breadth 26 cm.P, Q, R, and S are the midpoints of AB, BC,CD and AD respectively. If BD is the diagonal, what is the area (in cm) of the shaded

part?

Note*: Question does not include figure.

Solution: AB=CD=40 cm

AP=PB=RC=RD=20 cm(P and R are midpoint of AB and CD respectively)

BC=AD=26 cm

BQ=QC=DS=SA=13 cm

Area of Rectangle= Length×Breadth

= 40×26

= 1040 sq-cm

Area of ∆APS=Area of ∆PBQ=Area of ∆QRC=Area of ∆DSR

(All are right angle triangle,right angle at A,B,C and D respectively)

Area of ∆APS= 1/2×Base×Height

= 1/2×AS×AP

=1/2×13×20

=13×10

=130 Sq-cm

Area of all four triangles= 4×130

=520 sq-cm

Area of Shaded part(PQRS)= Area of ABCD- Area of four triangles.

= 1040-520

=520 sq-cm

Hope it helps you.