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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. - CBSE Class 9 - Mathematics

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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
[∡ Diagonal of a parallelogram divides into two congruent triangles]
= 2 ×[π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ Δ𝐴𝐡𝐢]
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`

∴π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘Žπ‘™π‘™π‘’π‘™π‘œπ‘”π‘Ÿπ‘Žπ‘š 𝐴𝐡𝐢𝐷=2[π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ Δ𝐴𝐡𝐢]=2×336=`672 cm^2`

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Solution 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. Concept: Area of a Triangle by Heron’S Formula.
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