A field is made up of a rectangle and two identical semicircles. The lenght of the rectangle is 200 m and the radius of each semicircle is 40 m. Find the perimeter and area of the field. (Take pie = 3.14.)
Answers
If the length of the rectangle is 200 m and the radius of each semicircle is 40 m, then the perimeter of the field is 811.2 m and area of the field is 21024 m².
Step-by-step explanation:
The length of the rectangle, l = 200 m
The radius of each semicircle, r = 40 m
Referring to the figure attached below, we can see that the diameter of each semicircle gives us the breadth of the rectangle, so,
The breadth of the rectangle = diameter of 1 semicircle = 2*r = 2*40 = 80 m
Case 1: Perimeter of the field
Perimeter of the rectangular part of the field = 2[l+b] = 2[200+80] = 560 m
And,
Perimeter of 2 semicircular parts of the field = 2 * [πr] = 2 * 3.14 * 40 = 251.2 m
Thus,
The perimeter of the field is given by,
= [Perimeter of the rectangular part of the field] + [Perimeter of 2 semicircular parts of the field]
= 560 m + 251.2 m
= 811.2 m
Case 2: Area of the field
Area of the rectangular part of the field = l*b = 200 * 80 = 16000 m²
And,
Area of 2 semicircular parts of the field = 2 * [(πr²)/2] = 3.14 * (40)² = 5024 m²
Thus,
The area of the field is given by,
= [Area of the rectangular part of the field] + [Area of 2 semicircular parts of the field]
= 16000 m² + 5024 m²
= 21024 m²
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