Find the area of the shaded region given in Fig. 11.20
Solution:
We have to find the shaded region from the given figure.
We observe ABCD is a square with a side 14 cm.
Join JK, KL, LM and JM.
So, JKLM forms a square
KEJ, JHM, MGL and LFK are four equal semicircles.
The dimension of FH = EG = 14 - 3 - 3
= 14 - 6
= 8 cm
The side of square JKLM will be 4 cm
The diameter of semicircle will be 4 cm
So, radius of the semicircle = 4/2 = 2 cm
Area of the shaded region = area of square ABCD - area of square JKLM - area of 4 semicircles
Area of square = (side)²
Area of square ABCD = (14)²
= 196 cm²
Area of square JKLM = (4)²
= 16 cm²
Area of semicircle = πr²/2
Area of semicircle KEJ = (22/7)(2)²/2
= (22/7)(2)
= 44/7
= 6.2857 cm²
Since all semicircles are equal.
Area of 4 semicircle = 4(area of one semicircle)
= 4(6.2857)
= 25.14286 cm²
Area of the shaded region = 196 - 16 - 25.14286
= 180 - 25.14286
= 154.857 cm²
Therefore, the area of the shaded region is 154.857 cm²
✦ Try This: ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC = 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 17
Find the area of the shaded region given in Fig. 11.20
Summary:
The area of the shaded region is 154.857 cm²
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