#### Question

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

#### Solution

Given that adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm.

Area of parallelogram = Area of ΔADC + area of ΔABC

[β΅ Diagonal of a parallelogram divides into two congruent triangles]

= 2 ×[π΄πππ ππ Δπ΄π΅πΆ]

Now for Area of ΔABC

Let 2s = AB + BC + CA [β΅ Perimeter of ΔABC]

`⇒S=1/2(AB+BC+CA)`

`=S=1/2(34+20+42)`

`=1/2=(96)=48cm`

∴Area of ΔABC =`sqrt(s(s-ab))`

`=sqrt(48(48-34)(48-20)(48-42))`

`=sqrt(48(14)(28)(6))=336 cm^2`

∴π΄πππ ππ πππππππππππππ π΄π΅πΆπ·=2[π΄πππ ππ Δπ΄π΅πΆ]=2×336=`672 cm^2`