Presentation on theme: "Lateral Area, Surface Area and Volume"— Presentation transcript:
1 Lateral Area, Surface Area and Volume Honors GeometryLateral Area, Surface Area and Volume
2 Prisms - definitionsA PRISM is any object with two parallel congruent bases with lateral sides that are parallelograms.In this case, the two pink sides are the bases.In this case, the two blue sides are the bases.In this case, the two yellow sides are the bases.The bases are not always on the top and bottom! In the next figure, the bases are the front and the back,because they are theparallel congruentsides.In this case, the two blue sides are the bases.In this case, the two blue sides are the bases.
3 Prisms are named by the shape of their bases. Naming PrismsPrisms are named by the shape of their bases.HexagonalPrismTriangularPrismRectangularPrismSquarePrism
4 Right and Oblique Prisms A right PRISM has the sides perpendicular to the bases.An oblique PRISM has sides that are NOT perpendicular to the bases.RightPrismObliquePrism
5 CylindersA CYLINDER is a special case of a prism where the two parallel sides (bases) are circles.A cylinder can be thought of as a circular prism.A right cylinder has its side perpendicular to its bases.An oblique cylinder has its side NOT perpendicular to its bases.
6 Lateral Area of a PrismLateral Area (LA) is the area of the side(s) of the object not including the bases.xyzzxyIn this case, the LA = (x + y + x + y) z,but x + y + x + y = 2x + 2y.This happens to be the perimeter of the base (P).So, the LA of a right prism is given by LA = Ph.
7 Lateral Area of a Cylinder I like to think of the LA of a cylinder as measuring the area of the label of a soup can. If you cut down the dotted line and peel the label off and lay it out flat, it is a rectangle. The base of the rectangle is the circumference of the base and the height of the rectangle is the height of the cylinder.hrCircumferenceHeightTherefore, LA of a cylinder is given by LA = Ch.Since circumference is to a circle as perimeter is to a polygon, this just a variation of LA = Ph.
8 Surface (Total) Area of a Prism The Surface area of a Prism is the sum of the area of ALL of the sides. It is also the LA plus the area of the two bases. Since, however the two bases are congruent, the surface area of a right prism (if B is the area of a base) is given by SA = LA + 2B
9 Example 1 Find the Surface Area LA = Ph; SA = LA + 2B LA = Ph; P = 2(12cm) + 2(10cm) = 44cm; h = 8cmLA = (44cm)(8cm) = 352cm2B = (12cm)(10cm) = 120cm2;so 2B = 2(120cm2) = 240cm2SA = LA + 2B = 352cm cm2 = 592cm2
10 Example 2 Find the Surface Area LA = Ph; SA = LA + 2B LA = Ph; P = 15 in in. + 9 in. = 36 in.; h = 13 in.LA = (36 in.)(13 in.) = 468 in.2B = 1/2(12 in.)(9 in.) = 54 in.2;so 2B = 2(54 in.2) = 108 in.2SA = LA + 2B = 468 in in.2 = 576 in.2
11 Surface Area of a Cylinder The Surface Area of a Cylinder is much like that of a Prism. It the LA + the area of the 2 bases or (since the bases are congruent), LA + twice the area of a base (B).SA = Ch + 2B
12 Example 3 Find the Surface Area LA = Ch; SA = LA + 2B LA = Ch; C = 2π(8 ft.) = 16π ft. = ft.; h = 12 ft.LA = (50.27 ft.)(12 ft.) = ft.2B = π(8ft.)2 = 64π ft.2 = ft.2;so 2B = 2( ft.2) = ft.2SA = LA + 2B = ft ft.2 = ft.2
13 Lateral Area and Surface Area AssignmentLateral Area and Surface Areaall