in the given figure ABC is an equilateral triangle . Two semi- circles with center O and P are drawn on sides AC and DC respectively as diameters . Find sum of the area of triangle ADC and the two semicircles
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Step-by-step explanation:
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
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