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## Prisms

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**Have 2 bases**Named by the shape of the bases Have 1 base Lateral faces meet at one point Named by the shape of the base Prisms Pyramids Pentagonal Prism Hexagonal Pyramid**Prisms**BASE HEIGHT BASE**Right Prism**Oblique Prism height**cylinder**Base Lateral Surface Height Base**Lateral Area (LA): the sum of the areas of the solid’s**lateral surfaces Total Surface Area (TA or SA): the sum of the areas of all of its surfaces P = PERIMETER of base (add all sides of the base) B = area of BASE (use different formulas according to the shape of the base) h = HEIGHT of the solid**Formulas for PRISMS**LA = PhLateral Area = Perimeter of Base height of prism SA = Ph + 2BSurface Area = Perimeter of Base height of prism + 2 Area of Base**EX:1 Find the lateral area.(One base is the side that is on**the ground.) 2.1 cm 3.6 cm 6.8 cm LA = Ph LA = 20.8 x 2.1 LA = 43.68 cm2**EX:2 Find the surface area.**2.1 cm 3.6 cm 6.8 cm SA = Ph + 2B SA = 43.68 + 2(24.48) SA = 92.64 cm2**EX:3 Find the lateral area.(One base is the side that is on**the ground.) LA = Ph 6 m LA = 24 x 9 8 m LA = 216 m2 9 m**EX:4 Find the surface area.(One base is the side that is on**the ground.) SA = Ph + 2B 6 m SA = 216 + 2(24) 8 m SA = 264 m2 9 m**Formulas for Cylinders**LA = 2rh SA = 2rh + 2r2**EX:5 Find the lateral area. Round to the nearest tenth.**5 cm 3.8 cm**EX:6 Find the surface area. Round to the nearest tenth.**5 cm SA = 2rh + 2r2 3.8 cm**Surface Area of Pyramids and ConesSection 12.3**Goal – to find the surface area of a pyramid and the surface area of a cone**Surface Area verses Lateral Area of a Pyramid**The lateral area of a pyramid: LA = P = Perimeter of the base l = slant height The surface area of a pyramid: SA = B = Area of the base**Surface Area verses Lateral Area of a Cone**The lateral area of a cone: LA = r = radius of the base l= slant height The surface area of a cone: SA =