Question

parallelogram ABCD and ABEF on the same base and between same parallels are equal.Show by figure​

Answer 1

Parallelogram ABCD and rectangle ABEF on same base AB have equal areas.           ....Given

AB=CD        ...opposite side of parallelogram

AB=EF         ...opposite side of rectangle

and, ∠F=∠E=90∘

AD>AF and BC>BE     ....(Hypotenuse of right angle is greater than other sides )

Now,

Perimeter of □ABCD=AB+BC+CD+DA

Perimeter of □ABEF=AB+BE+EF+FA 

Also, CD=EF and  AD>AF,BC>BE

∴ Perimeter of parallelogram ABCD> Perimeter of rectangle ABEF

Answer 2

Parallelogram

ABCD and rectangle ABEF on same base

AB

have equal areas. ....Given

AB=

CD

...opposite side of parallelogram

AB=

EF

...opposite side of rectangle

and,

∠F=

∠E=

90

∘

AD>

AF

and

BC>

BE

....(Hypotenuse of right angle is greater than other sides )

Now,

Perimeter of

□ABCD=

AB+

BC+

CD+

DA

Perimeter of

□ABEF=

AB+

BE+

EF+

FA

Also,

CD=

EF

and

AD>

AF,BC>

BE

∴ Perimeter of parallelogram ABCD> Perimeter of rectangle ABEF