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.

Answer 1

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
[∵ Diagonal of a parallelogram divides into two congruent triangles]
= 2 ×[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]
Now for Area of ΔABC
Let 2s = AB + BC + CA [∵ 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`

∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝐴𝐵𝐶𝐷=2[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]=2×336=`672 cm^2`