The area of the given parallelogram will be 762.14 inches².
What is a parallelogram?
A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
The parallelogram consists of two equal triangles with side lengths as shown in the figure.
Area of 1 triangle = [tex]\sqrt{s(s-a)(s-b)((s-c)}[/tex]
where s = (a+b+c)/2
So s = (31.9+24.3+36.4)/2 = 46.3
Now the area of the triangle will be
⇒ [tex]\sqrt{46.3(46.3-31.9)(46.3-24.3)(46.3-36.4)}[/tex]
⇒ 381.07 inches²
Now the area of parallelogram = 2× area of a triangle.
Area of parallelogram = 2 × 381.07 ⇒ 762.14 inches².
Hence the area of the parallelogram will be 762.14 inches².
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