Surface Area. Definitions: Surface Area – Is the sum of the areas of a three- dimensional figure’s surfaces. Net – Is the shape made when the surface.

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Presentation transcript:

Surface Area

Definitions: Surface Area – Is the sum of the areas of a three- dimensional figure’s surfaces. Net – Is the shape made when the surface of a three- dimensional figure is laid out flat showing each face of the figure. Pyramid – Is a three-dimensional figure with at least three triangular sides that meet a common point (called a vertex). Surface Area

Example 1: Find the surface area of the of the rectangular prism below by using a net. Find the area of each face of the prism. Final answer A = 11 5 = 55 in 2 B = = 231 in 2 C = 21 5 = 105 in 2 D = = 231 in 2 E = 21 5 = 105 in 2 F = 11 5 = 55 in 2 S = = = 782 in 2 The surface area of the rectangular prism is 782 in 2. Option 1: Using a Net Strategy: * For this option, we can use a net so that we can see each face of the prism. * Then, we can find the area of each face and add them together. Add the area of each side of the prism together. Surface Area of Rectangular Prism

Example 2: Find the surface area of the of the cube below by using a 3-D drawing. Find the area for the front, top and side of the figure and then multiply them by two. Final answer Front/Back: 6 8 = = 96 Top/Bottom: 6 4 = = 48 Sides: 4 8 = = 64 S = = = 208 cm 2 Option 2: Using a 3-Dimensional Drawing Strategy: * For this option, we will find the area of the front, top and side of the figure and multiply each by two to include the opposite faces. * Then, add all of the areas together. Add the areas together. The surface area of the rectangular prism is 208 cm 2. Surface Area of Rectangular Prism

Try these: Find the surface area of the rectangular prisms below. 1.2.) Surface Area

Example 3: Find the surface area of the of the pyramid below by using the formula. S = Area of Square + 4 (area of tri face) S.A.= s (bh) 2 S.A. = (6 5) 2 S.A. = S.A. = S.A. = 96 ft 2 Simplify The surface area of the pyramid is 96 ft 2. Surface Area of a Pyramid Substitute the side length (6), the base of the triangle (6) and the height of the triangle (50). Final answer Algebraic formula Formula

Example 4: Find the surface area of the of the cylinder below by using the formula. Formula S = 2 (area of each base) + Area of Curved Surface S.A. = 2 ( π r 2 ) + (2 π rh) S.A. = 2 ( ) + ( ) S.A. = 2 (3.14 4) + ( ) S.A. = 2 (12.56) S.A = S.A = in 2 Simplify The surface area of the cone about is ft 2. Surface Area of a Cone Algebraic formula Final answer Substitute necessary information.

Try these: Find the surface area of the figures below. 1.2.) Surface Area

A pyramid puzzle has all sides that are equilateral triangles. Each triangle has a side length of 8 cm. The slant height of the faces is 6.9 cm. Find the surface area of the puzzle. Real-World Application Surface Area