Find the Area of the figure.
Answers
Answer:
576 cm²
Step-by-step explanation:
We know that
Area of parallelogram = (1/2) × base × height
here base is AD = 48 cm (given)
we need to find height, ie, BE
The triangle AEB is a right angled triangle. Hence the pythagorean theorem is applicable here, ie, AB² = AE² + BE²
here, AB = 25 cm and AE = 7cm (as given in the figure)
Substituting,
AB² = AE² + BE²
25² = 7² + BE²
625 = 49 + BE²
625 - 49 = BE²
576 = BE²
√576 = BE
24 = BE
Hence height = BE = 24 cm
Now substituting value of height in Area of parallelogram formula,
Area of parallelogram = (1/2) × base × height
base = AD = 48 cm (given)
height = BE = 24 cm
∴ Area of parallelogram = (1/2) × 48 cm × 24 cm
⇒ 24 cm × 24 cm = 576 cm²
Hope it helps :D
Step-by-step explanation:
Given :-
In a Parallelogram ABCD , BC = 48 cm ,
AB = 25 cm and AE = 7 cm
To find :-
Find the area of the given Parallelogram ABCD?
Solution :-
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
Hypotenuse ² = Side ² + Side ²
=> 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
Answer:-
Area of the given Parallelogram ABCD is
1152 sq.cm
Used formulae:-
→ Area of a Parallelogram = bh sq.units
- b = base
- h = height
Used Theorem :-
Pythagoras Theorem:-
" In a right angled triangle , the square of the hypotenuse is equal to the sum of the squares of the other two sides ".
Points to know :-
→ Each side of the parallelogram is called its base.
→ Opposite sides are equal and parallel in a Parallelogram.