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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
[โต Diagonal of a parallelogram divides into two congruent triangles]
= 2 ×[๐ด๐๐๐ ๐๐ Δ๐ด๐ต๐ถ]
Now for Area of ΔABC
Let 2s = AB + BC + CA [โต 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`
∴๐ด๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐๐๐ ๐ด๐ต๐ถ๐ท=2[๐ด๐๐๐ ๐๐ Δ๐ด๐ต๐ถ]=2×336=`672 cm^2`
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