In figure ABC is a right-angled triangle in which ZA=90°, AB=21 cm and AC=28 cm. Semi-circles are
described on AB, BC, and AC as diameters. Find the area of the shaded region.
А
B
C
Answers
Answered by
1
Answer:775.25−481.25=294cm
Step-by-step explanation:
Area of shaded region = ar. semi-circle AB + ar. semi-circle AC + ar. △ABC - ar. semi-circle BC
=
2
π
[r
1
2
+r
2
2
]+
2
1
×AB×AC−
2
π
×r
3
2
=
2
1
×
7
22
[(
2
21
)
2
+(
2
28
)
2
]+
2
1
×21×28−
2
1
×
7
22
×(
2
BC
)
2
=
7
11
[
4
441
+
4
784
]+294−
7
11
×[
4
AB
2
+AC
2
]
=
7
11
×
4
1225
+294−
7
11
×
4
1
[21
2
+28
2
]=775.25−
28
11
×1225
=775.25−481.25=294cm
2
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