Surface Area Return to table of contents

Surface Area of Prisms Return to table of contents

Surface Area The sum of the areas of all outside surfaces of a 3-D figure. To find surface area, you must find the area of each surface of the figure then add them together. What type of figure is pictured? How many surfaces are there? How do you find the area of each surface? 6 in 3 in 8 in

Surface Area 6 in 3 in 8 in Bottom Top Left Right Front Back SUM 8 8 6 6 8 8 x 3 x 3 x 3 x 3 x 6 x 6 24 24 18 18 48 48 180 in2 8 in 6 in 6 in 3 in 8 in 6 in 3 in 3 in 8 in

Arrangement of Unit Cubes Find all the possible ways that 24 unit cubes can be arranged into a rectangular prism. Give each arrangements dimensions and surface area. Also make a sketch. Length Width Height Volume Surface Area Sketch

Which arrangement of 24 cubes has the least surface area? Which has the most? 6 possible arrangements 24 x 1 x 1 12 x 2 x 1 8 x 3 x 1 6 x 4 x 1 6 x 2 x 2 4 x 3 x 2 least: 4 x 3 x 2 = 54 u2 most: 24 x 1 x 1 = 98 u2

Arrangement of Unit Cubes Find all the possible ways that 64 unit cubes can be arranged into a rectangular prism. Give each arrangements dimensions and surface area. Also make a sketch. Length Width Height Volume Surface Area Sketch

Which arrangement of 64 cubes has the least surface area? Which has the most? 7 possible arrangements 64 x 1 x 1 32 x 2 x 1 16 x 4 x 1 8 x 8 x 1 16 x 2 x 2 8 x 4 x 2 4 x 4 x 4 least: 4 x 4 x 4 = 96 u2 most: 64 x 1 x 1 = 258 u2

Which arrangement of 27 cubes has the least surface area? 29 Which arrangement of 27 cubes has the least surface area? A 1 x 1 x 27 B 3 x 3 x 3 C 9 x 3 x 1 Answer: B

Which arrangement of 12 cubes has the least surface area? 30 Which arrangement of 12 cubes has the least surface area? A 2 x 2 x 3 B 4 x 3 x 1 C 2 x 6 x 1 D 1 x 1 x 12 Answer: A

Which arrangement of 25 cubes has the greatest surface area? 31 Which arrangement of 25 cubes has the greatest surface area? A 1 x 1 x 25 B 1 x 5 x 5 Answer: A

Which arrangement of 48 cubes has the least surface area? 32 Which arrangement of 48 cubes has the least surface area? A 4 x 12 x 1 B 2 x 2 x 12 C 1 x 1 x 48 D 3 x 8 x 2 E 1 x 2 x 24 F 4 x 3 x 4 Answer: F

Top/Bottom Front/Back Left/Right Surface Area 12 12 6 144 Find the surface area of a rectangular shoe box that has a length of 12 inches, a width of 6 inches and a height of 5 inches. 5 in 6 in 12 in Top/Bottom Front/Back Left/Right Surface Area 12 12 6 144 x 6 x 5 x 5 120 72 60 30 + 60 x 2 x 2 x 2 324 in2 144 120 60 click to reveal click to reveal click to reveal click to reveal

Find the figure's surface area. Name the figure. Find the figure's surface area. 3 m 5 m 7 m Teacher’s instructions: Rectangular Prism Base 4 Rectangles 3(5)(2) 3(7) 5(7) 3(7) 5(7) 30 21 35 35 21 Sum = 142 m2

How many faces does the figure have? 33 How many faces does the figure have? 2 m 4 m 6 m Answer: 6

34 How many area problems must you complete when finding the surface area? 2 m 4 m 6 m Answer: 6 3 (if you double)

What is the area of the top or bottom face? 35 What is the area of the top or bottom face? 2 m 4 m 6 m Answer: 8 (2)(4) 8 m2

What is the area of the left or right face? 36 What is the area of the left or right face? 2 m 4 m 6 m Answer: 12 (2)(6) 12 m2

What is the area of the front or back face? 37 What is the area of the front or back face? 2 m 4 m 6 m Answer: 24 (6)(4) 24 m2

What is the surface area of the figure? 38 What is the surface area of the figure? 2 m 4 m 6 m Answer: 88 2(8)+2(12)+2(24) 88 m2

Find the Surface Area. 1. Draw and label ALL faces 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 5 yd 6 yd 4 yd 5 yd go on to see steps 9 yd

Total Surface Area 24 54 + 90 168 yd2 Triangles Bottom Rectangle 4 9 CLICK TO REVEAL CLICK TO REVEAL Triangles Bottom Rectangle 4 9 x 6 x 6 24 / 2 = 12 54 x 2 24 CLICK TO REVEAL CLICK TO REVEAL Total Surface Area 24 54 + 90 168 yd2 9 yd 5 yd 6 yd 4 yd Left/Right Rectangles (Same size since isosceles) 5 x 9 45 x 2 90

Find the Surface Area. 1. Draw and label ALL faces 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 9 cm 6 cm 11 cm TRY THIS ONE

Click on box to reveal steps. 9 cm 6 cm 11 cm Triangles Rectangles Click on box to reveal steps. Answer: 351 cm2

Find the surface area of the shape below. 39 Find the surface area of the shape below. 1. Draw and label ALL faces 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 21 ft 42 ft 50 ft 47 ft Answer: 6382 ft2

Find the Surface Area. 7 cm 3 cm 4 cm 15 cm 6 cm 5 cm

Trapezoids 10 + 6 16 x 4 64 / 2 = 32 x 2 64 Bottom Rectangle 6 x 15 90 7 cm 3 cm 4 cm 15 cm 6 cm 5 cm Trapezoids 10 + 6 16 x 4 64 / 2 = 32 x 2 64 Bottom Rectangle 6 x 15 90 Top Rectangle 10 x 15 150 Side Rectangles 5 x 15 75 x 2 150 click to reveal click to reveal click to reveal click to reveal Surface Area 64 90 150 + 150 454 cm2 click to reveal

Find the surface area of the shape below. 40 Find the surface area of the shape below. Answer: Bases Sides 2 Triangles 3 Rectangles A = (1/2)bh x 2 10 x 9 = 90 A = (1/2)(8)(6) x 2 6 x 9 = 54 A = 48 cm2 8 x 9 = 72 sum = 216 cm2 Surface area = 264 cm2

Find the surface area of the shape below. 41 Find the surface area of the shape below. 10 cm 2 cm 6 cm Answer: Bases Sides Square & Rectangle 6 Rectangles A = s2 + lw 6 x 10 = 60 A = 62 + 4 x 2 6 x 10 = 60 A = 36 + 8 4 x 10 = 40 A= 44 cm2 4 x 10 = 40 A = 44 x 2 2 x 10 = 20 (top + bottom) 10 x 10 = 100 A = 88 cm2 sum = 320 cm2 SurfaceArea = 408 cm2