Question

ABCD is a parallelogram what is the area of ABCD?

Answer 1

Area of parallelogram = 432
`cm^2`.

Length of
`\overline{AC}`= 48 cm.

Explanation:

In the given figure I ABCD is a parallelogram

Base of parallelogram ABCD= AB=18 cm

Length of side BC= 30 cm

We know that

area of parallelogram=
`base* height`

Pythogorous theorem :

`(perpendicular\; side)^2+ (Base)^2= ( hypotenuse)^2`

`(BC)^2= (AB)^2+ (AC)^2`

`(30)^2=(18)^2+ (AC)^2`

900=324+
`(AC)^2`

`(AC)^2`=900-324=576

AC=
`√(576)`=24 cm

Length of side AC=24 cm

Area of parallelogram =
`18* 24`=432
`cm^2`.

In II figure

AD=26 cm

DB=10 cm

AB=BC ( given)

By using pythogorous theorem

In triangle ABD

`(AD)^2= (BD)^2+ (AB)^2`

`(26)^2= (10)^2+ (AB)^2`

676=100 +
`(AB)^2`

`(AB)^2`= 676-100=576

AB=
`√(576)`

AB=24 cm

AC=
`2* AB`

AC=
`2* 24`

AC=48 cm .