secant of the circle - Find the area of the shaded region in figure, where ABCD is a square of side 10 cm. and semicircles are drawn with each side of the square as diameter (use π = 3.14)

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Understand the question and figure

NOTE: Each semi circle has drawn with side of square as a diameter

Step 2: Name the un-shaded regions of the figure

Let Unshaded regions be 1, 2, 3 and 4

Step 3: Find the radius of the semicircle

NOTE: Diameter = 10

Radius = \frac{10}{2} = 5

Step 4: Evaluate the area of the square

EXAMPLE: Area of square = side^2

= 10^2

= 100

Step 5: Calculate the area of the semi-circle

NOTE: Area of the semicircle = \frac{1}{2} \pi r^2

EXAMPLE: = \frac{1}{2} * 3.14 * 5 * 5

= \frac{1}{2} * 3.14 * 25

Step 6: Find the areas of the un-shaded regions

NOTE: Area of 1 + Area of 3= Area of ABCD – Areas of two semicircles of each of radius 5 cm

= (100 - 3.14 * 25)

= (100 - 78.5)

=21.5 cm²

So,

Even the Area of 2 and 4 is equal to 21.5 cm²

Step 7: Determine the area of the shaded region

NOTE: Area of the shaded region = Area of ABCD - Area 0f ( 1+2+3+4)

EXAMPLE: Area of the shaded region = 100 - (21.5 + 21.5)

= 100 - 43

=57 cm^2