In the adjoining figure ABCD is a rectangle of area 98 cm2 . The length is twice the
breadth. Find the area of shaded region.
Answers
Answer :-
The area of shaded region is 96.25 cm².
Explanation :-
Given :
- Area of rectangle - 98 cm²
- Length = Twice the breadth
To find :
- The area of shaded region
Solution :
Let the breadth be 'x' & the length be '2x'
We know that,
Area of rectangle = Length × breadth
According to question,
=> 2x × x = 98
=> 2x² = 98
=> x² = 98/2
=> x² = 49
=> x = √49
=> x = 7
.°. Breadth = 7 cm & Length = 14 cm
Now,
Length of the rectangle = Diameter of the bigger circle
.°. Radius = Diameter/2 unit
= 14/2 cm
= 7 cm
Now, Area of half of the bigger circle :-
= 1/2 × π × r² sq. unit
= 1/2 × 22/7 × 7 × 7 cm²
= 77 cm²
Again,
Breadth of the rectangle = Diameter of the smaller circle
.°. Radius = Diameter/2 unit
= 7/2 cm
Now, Area of half of the smaller circle :-
= 1/2 × π × r² sq. unit
= 1/2 × 22/7 × 7/2 × 7/2 cm²
= 19.25 cm²
.°. Total area of shaded region :
= (77 + 19.25) cm²
= 96.25 cm²
Answer:
Answer :-
The area of shaded region is 96.25 cm².
Explanation :-
Given :
Area of rectangle - 98 cm²
Length = Twice the breadth
To find :
The area of shaded region
Solution :
Let the breadth be 'x' & the length be '2x'
We know that,
Area of rectangle = Length × breadth
According to question,
=> 2x × x = 98
=> 2x² = 98
=> x² = 98/2
=> x² = 49
=> x = √49
=> x = 7
.°. Breadth = 7 cm & Length = 14 cm
Now,
Length of the rectangle = Diameter of the bigger circle
.°. Radius = Diameter/2 unit
= 14/2 cm
= 7 cm
Now, Area of half of the bigger circle :-
= 1/2 × π × r² sq. unit
= 1/2 × 22/7 × 7 × 7 cm²
= 77 cm²
Again,
Breadth of the rectangle = Diameter of the smaller circle
.°. Radius = Diameter/2 unit
= 7/2 cm
Now, Area of half of the smaller circle :-
= 1/2 × π × r² sq. unit
= 1/2 × 22/7 × 7/2 × 7/2 cm²
= 19.25 cm²
.°. Total area of shaded region :
= (77 + 19.25) cm²
= 96.25 cm²