 # Surface Area What does it mean to you? Does it have anything to do with what is in the inside of the prism.? Surface area is found by finding the area.

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Surface Area What does it mean to you? Does it have anything to do with what is in the inside of the prism.? Surface area is found by finding the area of all the sides and then adding those answers up. How will the answer be labeled? Units 2 because it is area!

Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. A B C 4 5 in 6 Do any of the faces have the same area? A = 5 x 4 = 20 x 2 =40 B = 6 x 5 = 30 x 2 = 60 C = 4 x 6 = 24 x 2 = 48 If so, which ones? 148 in 2 Opposite faces are the same. Find the SA

Cube Are all the faces the same?YES 4m How many faces are there? 6 Find the Surface area of one of the faces. A 4 x 4 = 16Take that times the number of faces. X 6 96 m 2 SA for a cube.

Triangular Prism How many faces are there? 5 How many of each shape does it take to make this prism? 2 triangles and 3 rectangles = SA of a triangular prism 4 3 5 10 m Find the surface area. Start by finding the area of the triangle. 4 x 3/2 = 6 How many triangles were there? 2 x 2 = 12 Find the area of the 3 rectangles. 5 x 10 = 50 = front 4 x 10 = 40 = back 3 x 10 = 30 = bottom SA = 132 m 2 What is the final SA?

SA You can find the SA of any prism by using the basic formula for SA which is 2B + LSA= SA LSA= lateral Surface area LSA= perimeter of the base x height of the prism B = the base of the prism.

Triangular Prisms Use the same triangular prism we used before. Let’s us the formula this time. 2B + LSA=SA Find the area of the base, which is a triangle because it is a triangular prism. You will need two of them. Now, find the perimeter of that same base and multiply it by how many layer of triangles are in the picture. That is the LSA. Add that to the two bases. Now you should have the same answer as before. Either way is the correct way.

Cylinders 6 10m What does it take to make this? 2 circles and 1 rectangle= a cylinder 2 B3.14 x 9 = 28.26X 2 = 56.52 + LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4 SA = 244.92 2B + LSA = SA

 Why should you learn about surface area?  Is it something that you will ever use in everyday life?  If so, who do you know that uses it?  Have you ever had to use it outside of math?

Surface Areas of Pyramids

Pyramids Pyramid Pyramid – A three dimensional figure in which one face, the base, is any polygon and the lateral faces are triangles that meet at a common vertex. vertex

Pyramids cont. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is called the height. Height Pyramid

Pyramids cont. Regular Pyramid – a pyramid whose base is a regular polygon. Slant Height – the length of the altitude of the lateral face. Slant Height Pyramid

Formulas Lateral Area and Surface Area of a Regular Pyramid Later al Area Base Perime ter Slant Height Surfac e Area Lateral Area Base Area B

Example 1: Finding Surface Area of a Pyramid Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.

#3 Find the surface area of: 12 m

#4 Find the surface area of: 10” 15” 10” S = L + B S = ½ (40)(15) + (10)(10) S = 400 in 2

Surface Area of a Cone With slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of%20Pyramids %20and%20Cones%20C...

A cone has a circular base and a vertex that is not in the same plane as a base. In a right cone, the height meets the base at its center. The height of a cone is the perpendicular distance between the vertex and the base. The slant height of a cone is the distance between the vertex and a point on the base edge. Height Lateral Surface The vertex is directly above the center of the circle. Base r Slant Height r

Surface Area of a Cone Surface Area = area of base + area of sector = area of base + π(radius of base)(slant height) r

Lateral Area of a Cone Since Lateral Area = Surface Area – area of the base L.A. =

Example 1: Find the surface area of the cone to the nearest whole number. a.r = 4 slant height = 6 4 in. 6 in.

Example 2: Find the surface area of the cone to the nearest whole number. b. First, find the slant height. Next, r = 12, 12 ft. 5 ft.

On your own #1 Calculate the surface area of: S =  (7) 2 +  (7)(11.40) S = 49  + 79.80  S = 128.8 

On your own #2 Calculate the lateral area of: L.A. =  (5)(13) L.A. = 65  L.A. =

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