Mensuration Practice Test 1

Given ABCD is a rectangle

P, Q, R, S the mid points of

→

AB

,

→

BC

,

→

CD

,

→

DA

Join SQ in the given figure and Let AB = x and
AD = y; then the area of ΔPQS =

1

2

×x×

y

2

=

xy

4

and area of ΔSRQ =

1

2

×x×

y

2

=

xy

4

Area of Rhombus PQRS = Area of ΔPQR + Area of ΔSRQ =

xy

2

Hence, PQRS is a rhombus and its area is half of the area of rectangle ABCD ⇒

1

2

area (ABCD)