In the given figure, Triangle ABC is an equilateral triangle having each side equal to 10 cm and Triangle PBC is right angled at P in which PB = 8 cm. Find the area of the shaded region.
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Answer:
Given,△ABC and equilateral △BCD with AD=16cm and BC=8cm.
△ABC is a right angled triangle
∴AB
2
+BC
2
=AD
2
.......(Pythagoras Theorem)
AB
2
+8
2
=16
2
AB
2
=16
2
−8
2
=192
∴AB=
192
=8
3
cm.
Now, Area of △ABC =
2
1
× base × height
2
1
×AB×BC
=
2
1
×8
3
×8
=32
3
cm
2
Area of equilateral △BCD =
4
3
a
2
,where a is side of equilateral triangle.
=
4
3
×8
2
=16
3
cm
2
Area of shaded portion = Area of △ABC− Area of △BCD
=32
3
cm
2
−16
3
cm
2
=16
3
cm
2
=27.712cm
2
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