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**Volume of Rectangular and Triangular Prisms**

Geometry Volume of Rectangular and Triangular Prisms

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**Volume – the amount of space occupied by an object.**

Example: The VOLUME of this cube is all the space contained by the sides of the cube, measured in cube units (units3). h w l

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Volume Volume – To calculate the volume of a prism, we first need to calculate the area of the BASE of the prism. Example: The AREA of the base of this rectangular prism is l x w. h w l

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**Volume We find that: Volume = (l x w) x h**

Volume – Once we know the area of the base, this is then multiplied by the height to determine the VOLUME of the prism. We find that: Volume = Area of Base x Height Volume = (l x w) x h h w l

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**Volume (rectangular prism)**

Formula: V = B x h V = l x w x h h w l

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**Volume Formula: V = B x h V = l x w x h Find the volume of this prism…**

7 cm 4 cm 5 cm

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**Volume Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm**

Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm 7 cm 4 cm 5 cm

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**Volume Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm V = 140cm3**

Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm V = cm3 7 cm 4 cm 5 cm

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**Volume Formula: V = B x h V = l x w x h V = 7cm x 4cm x 5cm**

Does it matter which side is the base? Formula: V = B x h V = l x w x h V = 7cm x 4cm x 5cm 5 cm 4 cm 7 cm

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Volume Volume of a Triangular Prism

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**Volume The same principles apply to the triangular prism.**

To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow). h b

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**Volume To find the area of the Base… Area (triangle) = b x h 2**

This gives us the Area of the Base (B). h b

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**Volume Now to find the volume…**

We must then multiply the area of the base (B) by the height (h) of the prism. This will give us the Volume of the Prism. B h

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**Volume Volume of a Triangular Prism Volume (triangular prism)**

V = B x h B h

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Volume Together… Volume V = B x h

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Volume Together… Volume V = B x h V = (8 x 4) x 12 2

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Volume Together… Volume V = B x h V = (8 x 4) x 12 2 V = x 12

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**Volume Together… Volume V = B x h V = (8 x 4) x 12 2 V = 16 x 12**

V = cm3

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Volume Your turn… Find the Volume

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