the perimeter of square is equal to twice the perimeter of rectangle of length 10cm and breath 4cm. what is the circumference of a semicircle. whose diameter is equal to the side of the square.
Answers
Circumference Of Semicircle = 36 cm
Step-by-step explanation:
GIVEN
Length = 10 cm
Breadth = 4 cm
Perimeter Of Square = 2 × Perimeter Of Rectangle
Diameter Of Semicircle = Side Of Square
___________________________
TO FIND
Circumference Of Semicircle
___________________________
We know that,
Perimeter Of Rectangle = 2 × ( Length + Breadth )
Perimeter Of Rectangle = 2 × ( 10 + 4 )
Perimeter Of Rectangle = 2 × 14
Perimeter Of Rectangle = 28
Perimeter Of Rectangle = 28 cm
___________________________
We know that,
Perimeter Of Square = 2 × Perimeter Of Rectangle
Perimeter Of Square = 2 × 28
Perimeter Of Square = 56
Perimeter Of Square = 56 cm
___________________________
We know that,
Perimeter Of Square = 4 × Side
56 = 4 × Side
Side = 56 / 4
Side = 14
Side = 14 cm
___________________________
We know that,
Diameter Of Semicircle = Side Of Square
Diameter Of Semicircle = 14
Diameter Of Semicircle = 14 cm
___________________________
We know that,
Circumference Of Semicircle = ½ × ( π × d ) + d
Circumference Of Semicircle = ½ × ( 22/7 × 14 ) + 14
Circumference Of Semicircle = ½ × ( 22 × 2 ) + 14
Circumference Of Semicircle = ½ × 44 + 14
Circumference Of Semicircle = ½ × 44 + 14
Circumference Of Semicircle = 22 + 14
Circumference Of Semicircle = 36