Given info:- In a Parallelogram ABCD , BC = 48 cm ,
AB = 25 cm and AE = 7 cm. And here we have to find the area of the given Parallelogram ABCD?
Step-by-step explanation:-
In a Parallelogram ABCD ,
- BC = 48 cm
- AB = 25 cm
- AE = 7 cm
And
∆ AEB is a right angled triangle
Right angle at E
AB is the hypotenuse
We know that
By, Pythagoras theorem
Hypotenuse² = Side² + Side²
⇛ AB² = AE²+ BE²
⇛ 25² = 7² + BE²
⇛ 625 = 49 + BE²
⇛ BE² = 625-49
⇛ BE² = 576
⇛ BE = ±√576
⇛ BE = ±24
Since the length of the side cannot be negative
⇛ BE = 24 cm
⇛ BC = AD
⇛ AD = 48 cm
⇛ AE + ED = 48 cm
⇛ 7+ED = 48 cm
⇛ ED = 48-7
⇛ ED = 41 cm
We know that
Area of a Parallelogram = bh sq.units
Area of the given Parallelogram ABCD
⇛ AD × BE or BC × AE
⇛ 48 × 24 sq.cm
⇛ 1152 sq.cm
Therefore, the area of the given Parallelogram ABCD is 1152 sq.cm
Additional comment:
Each side of the parallelogram is called its base.
Opposite sides are equal and parallel in a Parallelogram.
If you have any doubt, then you can ask me in the comments.