12-1

Prisms

Notes•A Prism is a 3D solid with two congruent sides called bases

•The bases are in parallel planes

•Other sides are called lateral faces

•In between the lateral faces are lateral edges

•The Surface Area or Total Area of the sum of all its faces

•The Lateral Area is the sum of all its lateral faces

Notes

Notes

The Lateral Area of a right prism

L.A. = Ph

The Surface Area or Total Area of a right prism

T.A. = L.A. + 2B

Notes

Theorem 12-2

EXAMPLE 2 Find volumes of prisms and cylinders

Find the volume of the solid.

a. Right trapezoidal prism

SOLUTION

(3)(6 + 14)a. The area of a base is 12

= 30cm2 and h = 5 cm.

V = Bh = 30(5) = 150cm3

EXAMPLE 3 Use volume of a prism

ALGEBRA

The volume of the cube is 90 cubic inches. Find the value of x.

SOLUTION

A side length of the cube is x inches.

V = x3

90 in3. = x3

4.48 in. ≈ x

Formula for volume of a cube

Substitute for V.

Find the cube root.

SPICSA• 478 2-18 even