1. Surface Area

2. 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

3. 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 = 21 11 = 231 in 2 C = 21 5 = 105 in 2 D = 21 11 = 231 in 2 E = 21 5 = 105 in 2 F = 11 5 = 55 in 2 S = 55 + 231 + 105 + 231 + 105 + 55 = = 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

4. 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 = 48 48 2 = 96 Top/Bottom: 6 4 = 24 24 2 = 48 Sides: 4 8 = 32 32 2 = 64 S = 96 + 48 + 64 = = 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

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

6. 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 2 + 4 (bh) 2 S.A. = 6 2 + 4 (6 5) 2 S.A. = 36 + 4 15 S.A. = 36 + 60 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

7. 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 (3.14 2 2 ) + (2 3.14 2 5) S.A. = 2 (3.14 4) + (2 3.14 2 5) S.A. = 2 (12.56) + 62.8 S.A = 25.12 + 62.8 S.A = 87.92 in 2 Simplify The surface area of the cone about is 87.92 ft 2. Surface Area of a Cone Algebraic formula Final answer Substitute necessary information.

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

9. 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