Question

The length of the adjacent sides a parallelogram are 51cm ans 37cm. One of it's diagonal is 20cm, Find the area of the parallelogram.

Answer 1

Dear Student,

Let the two adjacent sides of the parallelogram be a = 51 cm, b = 37 cm
Let the length of diagonal be c = 20 cm
Diagonal of a parallelogram divided it into 2 congruent triangles.
These two sides and the diagonal forms a triangle
$$\begin{gathered} Semi-perimeter\left(s\right)=\frac{a+b+c}{2} \\ s=\frac{51+37+20}{2}=54cm \\ Byheron\text{'}sformula,Areaoftriangle=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ Areaoftriangle=\sqrt{54\left(54-51\right)\left(54-37\right)\left(54-20\right)} \\ Areaoftriangle=\sqrt{54\times 3\times 17\times 34} \\ Areaoftriangle=306c{m}^2 \\ Areaofparalle\log ram=2\times Areaoftriangle=2\times 306=612c{m}^2 \end{gathered}$$

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