Semi -circular lawns are attached to all the edges of a rectangular field measuring 42m ×35m.Find the area of the total field.
Answers
Answer:
3818.5 m²
Step-by-step explanation:
As the semicircular lawn is attached to all the edges of a rectangular field... on each side you are actually getting two circles with diameter 42m and 35m
Hence to find the perimeter you need circumference of the two circles.
Let the bigger circle with diameter 42m be C1 and the smaller circle with diameter 35m be C2
therefore,
radius of C1 = 42/2 = 21m
radius of C2 = 35/2 = 17.5m
circumference of C1 = 2 π r
= 2 * 22/7 * 21
= 132m
circumference of C2 = 2 π r
= 2 * 22/7 * 17.5
= 35 * 22/7
= 110m
therefore the perimeter of the total field = 132 + 110
= 242m
to find the area of the total field we need to add the areas of both the circles and the rectangle.
therefore,
area of C1 = π r²
= 22/7 × 21²
= 22/7 × 21× 21
= 22 × 21 × 3 (7 × 3 = 21)
= 1386m²
area of C2 = π r²
= 22/7 × 17.5 × 17.5
= 385/7 × 17.5 (22 × 17.5)
= 55 × 17.5
= 962.5m²
area of the rectangular field (R1) = l × b
= 42 × 35
= 1470m²
therefore the area of total field = C1 + C2 + R1
= 1386 + 962.5 + 1470
= 3818.5m²