Each side of triangle \(ABC\) is extended such that \(AB=BP, BC=CQ, CA=AR,\) as shown in the diagram above.
If the area of triangle \(ABC\) is 10, then what is the area of triangle \(PQR?\)
(1/2) AB * BC sin ABC + (1/2) BC * AC sin ACB + (1/2) AC* AB sin CAB = 30 = 3 times area of ABC =
(1/2) ( AB * BC sin ABC + BC * AC sin ACB + AC * AB sin CAB) = 30
sin AB * BC sin ABC + BC * AC sinACB + AC* AB sin CAB = 60
sin ABC = sin PBQ sin ACB = sin RCQ sin CAB = sinRAP
Pink area =
(1/2) AB ( BC + BC)sin ABC + (1/2) BC ( AC + AC)sin ACB + (1/2) AC (AB + AB) sin CAB =
AB * BC sin ABC + BC * AC sin ACB + AC* AB sin CAB = 60
So [ PQR ] = 10 + 60 = 70