a right angled triangle ABC, right angled at B, a semi- circle is drawn with AC as diameter ifAB=BC=7cm then find the area of the shaded region?
I
Answers
Answered by
0
△ABC is a right angled triangle. So, by Pythagoras theorem
AC
2
=AB
2
+BC
2
=7
2
+7
2
=98
∴AC=
98
=7
2
cm
Arc A−B−C is a semicircle. ∴AC=7
2
cm is the diameter of the semicircle.
Area of the shaded portion = Area of semi-circle (A−B−C)− Area of △ABC
=
2
1
×
4
πd
2
−
2
1
×AB×BC
=
2×7×4
22×98
−
2
7×7
=14 cm
2
Answered by
0
Answer:
In △ABC,∠A=90
o
By Pythagoras theorem,
BC
2
=AB
2
+AC
2
3
2
+4
2
9+16=25
∴BC=5cm
A(shadded region)=A(△ ABC)+A (semicircle AB) + (semicircle AC) - A(semicircle BAC)
=
2
1
×3×4+
2
1
×π(
2
3
)
2
+
2
1
×π(
2
4
)
2
−
2
1
×π(
2
5
)
2
=6+
8
6π
+2π−
8
25π
=6+2π−2π
=6cm
2
Similar questions