Surface Area What does it mean to you?, Does it have anything to do with what is in the inside of figure? 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!
Surface Area Steps for Finding Surface Area 1. Draw and label each face of the solid as if you had cut the solid apart along its edges and laid it flat. Label the dimensions. 2. Calculate the area of each face. If some faces are identical, you only need to find the area of one. 3. Find the total area of all the faces.
In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms. PRISM
In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms. PRISM In a pyramid, the base can be any polygon. The lateral faces are triangles. PYRAMID
Side 2 Bottom Back Top Side 1 Front Side 2 Bottom Back Top Side 1 Front Rectangular Prism
H H H H B H B H H Rectangular Prism Net B B B B
Example: Find the surface area of this rectangular prism Surface Area of a Prism It is made by: 2 congruent bases, and 4 lateral faces Calculate the area of each face. If some faces are identical, you only need to find the area of one. Then, find the total area of all the faces. Base area = 2(6 x 8) = 96 m2m2 Lateral surface area (front and back) = 2 (3x6) = 36 m2m2 Lateral surface area (sides) = 2 (3x8) = 48 m2m2 Surface area = 96 + 36 + 48 = 180 m2m2 Surface area 180 m 2
Rectangular Prism How many faces are on here?6 Find the area of each of the faces. A 4 in 5 in 6 in Do any of the faces have the same area? A = 5 x 4 = 20 x 2 = 40 C = 6 x 5 = 30 x 2 = 60 B = 4 x 6 = 24 x 2 = 48 If so, which ones? Surface Area = 40 + 48 + 60 = 148 in 2 Opposite faces are the same. Find the SA Surface Area of a Rectangular Prism 2A + 2B + 2C Surface Area of a Rectangular Prism 2A + 2B + 2C
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 area of the triangle. 4 x 3/2 = 6 How many triangles were there? 22 x 2 = 12 What is the final SA? Area of bases + area of laterals = SA 12 + 120 = 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. 4 x 4 = 16Take that times the number of faces. x 6 96 m 2 SA for a cube. Surface Area of a Cube = 6 a 2
Example: Find the surface area of the cylinder Surface Area of a cylinder It is made by: 2 congruent circles, and 1 rectangle The two bases are circular regions, so you need to find the areas of two circles The lateral surface is a rectangular region The height of the rectangle is the height of the cylinder The base of the rectangle is the circumference of the circular base Circle area = 3.14 (5) 2 78.5 x 2 157 in 2 Cylinder surface area = 157 + 376.8 = 533.8 in 2 Lateral area = (2 x 3.14 x 5 )12 376.8 in 2 b= c = 2 r h= 12
Cylinders 10m What does it take to make this? 2 circles and 1 rectangle = SA cylinder SA = 56.52 + 188.4 2B + LSA = SA 3 2 circles (bases) 1 rectangle (Lateral) SA = 244.52
CLASS WORK Find the surface area of each solid. All given measurements are in centimeters
PYRAMID The surface area of a pyramid is the area of the base plus the areas of the triangular faces(lateral area). Slant height : It ist he height of each triangular lateral face. It is labeled l The pyramid height is labeled h. Surface Area Lateral Area Base Area SA = L+B
PYRAMID The surface area of a pyramid is the area of the base plus the areas of the triangular faces. What is the area of each lateral face? What is the area of the base for any regular n-gon pyramid? What is the total lateral surface area for any pyramid with a regular n-gon base The formula for the surface area of a regular n-gon pyramid in terms of n, base length b, slant height l, and apothem a. The formula for the surface area of a regular n-gon pyramid in terms of n, base length b, slant height l, and apothem a. _1_ bl 2 n. _1_ bl 2 1 aP or 1 abn 2 2 SA = 1 nb(l+a) 2 2
PYRAMID SA= 1 P(l+a) 2 2 The expression for the surface area of a regular n-gon pyramid in terms of height l, apothem a, and perimeter of the base, P.P.
PYRAMID The formulas to find the surface area of a pyramid are: SA = 1 P(l+a) 2 2 in terms of : l = height, a = apothem, and, P = perimeter of the base. or in terms of : n = number of triangular faces b = base length, l= slant height and a = apothem in terms of : n = number of triangular faces b = base length, l= slant height and a = apothem SA = 1 nb(l+a) 2 2 SA = L+B Basic formula
Spheres Sphere – The set of all points in space equidistant from a given point. Center r Radius – Is a segment that has one end point at the center & the other end point on the sphere. Diameter – A segment passing through the center w/ both end points on the sphere.
lateral surface Base = πr 2 r l l lateral surface= πrl
πrl πr 2 Where, r is the radius l is the slant height The surface area is the sum of the area of its base and the lateral (side) surface. CONES Find the area of the circle, or base Find the area of the curved (lateral) surface cone The surface area of the cone equals the area of the circle plus the surface area of the cone given by r l