7. Find the perimeter and area of each of the following shapes represented bold
(ii)
Answers
The perimeter of the shape represented bold lines is 90 cm.
The area of the shape represented bold lines is 544.25 cm².
Step-by-step explanation:
From the given figure, we get
The length of the rectangular shape = 21 cm
The breadth of the rectangular shape = 14 cm
Also, we can see that the diameter of bigger semi-circular portion is given by the length of the rectangular shape and similarly the diameter of smaller semi-circular portion is given by the breadth of the rectangular shape.
So, we will get
The radius of the bigger semi-circular portion, R = cm
The radius of the smaller semi-circular portion, r = cm = 7 cm
Case 1: Perimeter of the shape represented by the bold lines in the figure
The perimeter of the shape represented by the bold lines is given by,
= [Perimeter of the rectangular part in bold lines] + [Perimeter of the bigger semicircular part in bold lines] + [Perimeter of the smaller semicircular part in bold lines]
= 14 cm + [πR] cm + [πr] cm + 21 cm
= 14 + [ * ] + [ * 7] + 21
= 14 + 33 + 22 + 21
= 90 cm
Case 2: Area of the shape represented by the bold lines in the figure
The area of the shape represented by the bold lines is given by,
= [Area of the rectangular part in bold lines] + [Area of the bigger semicircular part in bold lines] + [Area of the smaller semicircular part in bold lines]
= [14*21] + [π(R²)/2] + [π(r²)/2]
= 294 + [ * * * ½ ] + [ * 7 * 7 * ½]
= 294 + 173.25 + 77
= 544.25 cm²
Thus, the perimeter and area of the given shape represented by bold lines are 90 cm and 544.25 cm^2 respectively.
--------------------------------------------------------------------------------------------