A triangle has side lengths 18 cm, 24 cm and 30 cm. find the area of the triangle whose vertices are the incenter, circumcenter and centroid of that triangle.

Explanation

`18^2 + 24^2 = 30^2`

`A(0,0) ,B(18,0) , C(0,24)`

centroid = `((0+0+18)/3, (24+0+0)/3)`

`= (6,8)`

circumcenter = MP of BC = `(18/2, 24/2) = (9,12)`

incenter (r) =` (area)/((1/2)perimeter)`

area = `1/2*24*18 = 216`

perimeter= `18+24+30 = 72`

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