In the following figure find the area of the shaded region. (Use π = 3.14)
Answers
Answer:
The area of shaded region is 154.88 cm².
Step-by-step explanation:
GIVEN :
Side of a square = 14 cm
There are four equally semi circles and JKLM formed the square.
FH = 14 - (3+3) = 14 - 6 = 8 cm
FH = 8 cm
Let the side of a square JKLM be x cm.
FH = x/2 + x + x/2
8 = x/2 + x/2 + x
8 = x + x
2x = 8
x = 8/2
x = 4 cm
so, the side of a square should be 4 cm and radius of semicircle of both ends are 2 cm each
Area of square JKLM = side²
= 4² = 16 cm²
Area of square JKLM = 16cm²
Area of semicircle JHM = ½ × πr²
= ½ × 3.14 × 2²
= ½ × 3.14 × 4
= 3.14 × 2
= 6.28 cm²
Area of semicircle JHM = 6.28 cm²
Area of square ABCD = 14² = 196 cm²
Area of shaded region = Area of a square ABCD - (Area four semicircles + Area of square JKLM)
= 196 - ( 4 × 6.28 + 16)
= 196 - (25.12 + 16)
= 196 - 41.12
= 154.88 cm²
Area of shaded region = 154.88 cm²
Hence, the area of shaded region is 154.88 cm².
HOPE THIS ANSWER WILL HELP YOU….
Here are more questions of the same chapter :
In the following figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:
(i)the circumference of the central part.
(ii)the perimeter of the part ABEF.
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In the following figure, ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180° have been cut off. Calculate:
(i)the area of the shaded region.
(ii)the length of the boundary of the shaded region.
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Answer:
answer is 27.93cm sq..
hope it will help you.....