The perimeter of the triangular base of a right prism is

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The perimeter of the triangular base of a right prism is 15 cm and radius of the incircle of the triangular base is 3 cm. If the volume of the prism be 270 cm³, then the height of the prism is

Radius of the in-circle = OE = OD = OF = 3 cm

Area of triangular base =		1	AB × OF +	1	× BC × OD +	1	× AC × OE
		2		2		2

=	1	× 3(AB + BC + AC) =	1	× 3 × 15 =	45	sq.cm.
	2		2		2

Volume of the prism = Area of the base × height

⇒ 270 =	45	× height
	2

∴ height =	270 × 2	= 12 cm.
	45