To find the perimeter and area of the shaded part, we need to calculate the lengths of the curves involved.
a) Perimeter of the shaded part:
The length of the semicircle ADC is half the circumference of the circle with radius OA, which is half the length of AB.
Length of ADC = (1/2) * 2π * (AB/2) = π * (AB/2) = (22/7) * (56/2) = 22 * 28 cm = 616 cm
The length of the semicircle BCE is also equal to the length of ADC.
Length of BCE = Length of ADC = 616 cm
The length of the quadrant ADF is one-fourth the circumference of the circle with radius OA.
Length of ADF = (1/4) * 2π * (AB/2) = (1/4) * 2 * (22/7) * 28 = 22 cm
The length of the quadrant BEC is also equal to the length of ADF.
Length of BEC = Length of ADF = 22 cm
The length of the shaded part is the sum of the lengths of ADC, BCE, ADF, and BEC.
Perimeter of shaded part = ADC + BCE + ADF + BEC = 616 + 616 + 22 + 22 = 1276 cm
b) Area of the shaded part:
The area of the semicircle ADC is half the area of the circle with radius OA.
Area of ADC = (1/2) * π * (AB/2)^2 = (1/2) * (22/7) * (28/2)^2 = (22/7) * (14)^2 = 308 cm²
The area of the semicircle BCE is also equal to the area of ADC.
Area of BCE = Area of ADC = 308 cm²
The area of the quadrant ADF is one-fourth the area of the circle with radius OA.
Area of ADF = (1/4) * π * (AB/2)^2 = (1/4) * (22/7) * (28/2)^2 = (22/7) * (14)^2 = 154 cm²
The area of the quadrant BEC is also equal to the area of ADF.
Area of BEC = Area of ADF = 154 cm²
The area of the shaded part is the sum of the areas of ADC, BCE, ADF, and BEC.
Area of shaded part = ADC + BCE + ADF + BEC = 308 + 308 + 154 + 154 = 924 cm²
Therefore, the perimeter of the shaded part is 1276 cm, and the area of the shaded part is 924 cm².