Find the area of shaded portion?
Answers
Step-by-step explanation:
Solution :-
From the given figure,
ABCD is a rectangle .
Length of the rectangle = AB = CD
= 12 cm
Breadth of the rectangle = AD = BC
= 5 cm
We know that
Area of a rectangle = length × breadth sq.units
Area of the rectangle ABCD
= AB×BC = CD× AD sq.cm
= 12×5 cm²
= 60 cm²
Area of the rectangle = 60 cm²
and
∆ABC is a right angled triangle
AC is the hypotenuse
AC = 13 cm
=> Diameter of the circle = AC
=> Diameter of the circle = 13 cm
We know that
Radius = Diameter /2
=> Radius of the circle = 13/2 cm
We know that
Area of a circle whose radius is r units is πr² sq.units
Area of the given circle
=> A = (22/7)×(13/2)² cm²
=> A = (22/7)×(13/2)×(13/2)
=> A = (22×13×13)/(7×2×2)
=> A = 3718/28
=> A = 1859/14
=> A = 132.7857...
=> A = 132.79 cm² (approximately)
Area of the circle = 132.79 cm²
Now,
Area of the shaded region
= Area of the circle - Area of the rectangle
= 132.79 cm² - 60 cm²
= 72.79 cm²
Therefore, required area = 72.79 cm²
Answer:-
Area of the shaded portion is 72.79 cm²
Used formulae:-
→ Area of a rectangle = length × breadth sq.units
→ Area of a circle whose radius is r units is πr² sq.units
→ π = 22/7
→ If a rectangle is inscribed in a circle then the diagonal of the rectangle is the diameter of the circle.
Refer the given attachment
