Surface Area
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? • Units2 because it is area!
B C 5 in A 6 4 Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. Do any of the faces have the same area? A = 5 x 4 = 20 x 2 =40 If so, which ones? B = 6 x 5 = 30 x 2 = 60 C = 4 x 6 = 24 x 2 = 48 Opposite faces are the same. 148 in2 Find the SA
Cube Are all the faces the same? YES A How many faces are there? 4m 6 Find the Surface area of one of the faces. 4 x 4 = 16 Take that times the number of faces. X 6 96 m2 SA for a cube.
Triangular Prism How many faces are there? 4 5 5 How many of each shape does it take to make this prism? 10 m 3 2 triangles and 3 rectangles = SA of a triangular prism Find the surface area. Start by finding the area of the triangle. x 2= 12 4 x 3/2 = 6 How many triangles were there? 5 x 10 = 50 = front 4 x 10 = 40 = back 3 x 10 = 30 = bottom 2 Find the area of the 3 rectangles. SA = 132 m2 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 What does it take to make this? 6 10m 2 circles and 1 rectangle= a cylinder 2B + LSA = SA 2 B 3.14 x 9 = 28.26 X 2 = 56.52 + LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4 SA = 244.92
SURFACE AREA • 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 – 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 Pyramid
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 Lateral Area Base Perimeter Slant Height B Surface Area Lateral Area Base Area
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
15” 10” 10” #4 Find the surface area of: S = L + B S = ½ (40)(15) + (10)(10) S = 400 in2
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. The vertex is directly above the center of the circle. Height Lateral Surface Slant Height r Base r
Surface Area of a Cone • Surface Area = area of base + area of sector = area of base + π(radius of base)(slant height) r
L.A. = Lateral Area of a Cone • Since Lateral Area = Surface Area – area of the base
Example 1: 4 in. • Find the surface area of the cone to the nearest whole number. a. r = 4 slant height = 6 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, 5 ft. 12 ft.
On your own #1 Calculate the surface area of: • S = (7)2 + (7)(11.40) • S = 49 + 79.80 • S = 128.8
L.A. = On your own #2 Calculate the lateral area of: • L.A. = (5)(13) • L.A. = 65
