SURFACE AREA OF A RECTANGULAR PRISM

Transcription

1 SURFACE AREA OF A RECANGULAR PRISM Objective: Find the surface area of a rectangular prism Review Find the area of the following plane figures. notebook. Write your answers on your 1. A = 5 dm 12 dm 2. A = 4 dm 6 dm 3. A = 17 cm 7 cm 4. A = 8.2 mm 4.3 mm 5. A = 5 m 7 m 1

2 Study and Learn Read the problem. he surface area of a solid figure is the sum of the areas of all its faces. he surface area of a rectangular solid which is also called rectangular prism is the sum of the areas of all the faces. length = 10 cm height = 3 cm width = 5 cm How many faces does the figure have? (6) How many vertices are there? (8) How many edges are there? (12) What can you say about the faces? Are they all the same? (No) o visualize clearly the faces of the rectangular prism, we will unfold the figure. SIDE (E) 10 cm F R O N (A) O P (B) B A C K (C) B O O M (D) 10 cm 3 cm 5 cm 3 cm SIDE (F) 5 cm 3 cm Which pairs of faces are the same in size and shape? (Front and Back; op and Bottom; right side and left side) What plane figures do the faces of rectangular prism represent? (rectangle) How do you get the area of a rectangle? (A = base x height or length x width) o find the surface area of the figure, we need to find the sum of the areas of the 6 faces of the rectangular prism. 2

3 Face Area of Face (cm 2 ) A 10 x 3 = 30 B 10 x 5 = 50 C 10 x 3 = 30 D 10 x 5 = 50 E 5 x 3 = 15 F 5 x 3 = 15 OAL 190 he surface area of the figure is 190 cm 2. We can also solve the same problem this way: We know that: 1. the bottom and top faces have the same dimensions, 10 cm by 5 cm 2. the left and right faces (sides) have the same dimensions, 5 cm by 3 cm 3. the front and back faces have the same dimensions, 10 cm by 3 cm Using the area formula for a rectangle, A = bh, we have 1. for bottom and top faces A = (10)(5) = 50 cm 2 50 x 2 = 100 cm 2 2. for left and right faces (sides) A = (5)(3) = 15 cm 2 15 x 2 = 30 cm 2 3. for front and back faces A = (10)(3) = 30 cm 2 30 x 2 = 60 cm 2 Adding these areas to find the surface area, we have 100 cm 2 bottom and top 30 cm 2 left and right 60 cm 2 front and back 190 cm 2 surface area 3

4 Is this the same answer as the one obtained earlier? o solve for the surface area of a rectangular prism, we can use a formula. SA = 2(lw) + 2(wh) + 2(lh) or 2 (lw + wh + lh) Where SA = surface area l = length w = width h = height For the example we did earlier: l = 10 cm; w = 5 cm; h = 3 cm SA = 2(lw) + 2(wh) + 2(lh) = 2(10)(5) + 2(5)(3) + 2(10)(3) = 2(50 cm 2 ) + 2(15 cm 2 ) + 2(30 cm 2 ) = 100 cm cm cm 2 = 190 cm 2 SA = 2(lw + wh + lh) = 2[(10)(5) + (5)(3) + (10)(3)] = 2( ) = 2(95 cm 2 ) = 190 cm 2 Which method is easiest for you? Do you want to try using that method? Let s answer the exercises under using that method. ry hese A. Find the surface area of the following rectangular prisms. Write your answer on your notebook. 1) E 4 cm A B C D 4 cm 1 cm F 1 cm 3 cm 3 cm 4

5 2) 5 cm P Q R S 5 cm 4 cm 4 cm 2 cm U 4 cm 4 cm 2 cm 3) 2.1 m 5.3 m 8.4 m 4) 5) 8 dm 7 dm 5 dm 7 m 11 m 3 m B. Complete the following charts. Copy and answer on your notebook. Rectangular Prism Area of Each Face (m 2 ) otal Surface Length Width Height Front Back Left Right op Bottom Area 1) 9 m 4 m 7 m 2) 3.4 m 1.6 m 7.2 m 3) 10 m 4 m 8 m 4) 7 m 8 m 12 m 5) 5 m 11 m 9 m C. Find the surface area of each box. Write the letter of the correct answer corresponding to the surface area in the box. 1) 2) 3) l = 9 m w = 6 m h = 8 m l = 11 w = 12 h = 10 l = 12 w = 7 h = 4 5

6 4) 5) l = 5 w = 7 h = 3 l = 14 w = 12 h = 13 SURFACE BOARD (m 2 ) A G E R S 142 1, Wrap Up he surface area of a solid figure is the sum of the areas of all its faces. he surface area of a rectangular prism is the sum of the faces of its 6 faces. We have two ways of getting the surface area of a rectangular prism. One is by unfolding the figure and finding the area of each faces then adding all of these. Another is by using the formula, SA = 2(lw) + 2(wh) + 2(lh) or 2(lw + wh + lh). 6

7 On Your Own A. Find the surface area of each of the following figures. Write your answer on your notebook dm 23 cm 6 m 20 cm 4 m 8 dm 25 cm 8 m 5 dm B. Find the surface of the following prisms. Write your answer on your notebook. 1) 4) 5 cm 7 dm 5 dm 4 cm 3 cm 12 dm 2) 5) 3 mm 5 cm 6 cm 21 mm 12 mm 4 cm 3) 8 mm 15 mm 5 mm 7

8 C. Read, analyze and solve. Write your answer on your notebook. 1. A wooden cabinet needs repainting. How much surface area needs to be painted if the box has a length of 75 cm, width of 45 cm, and height of 35 cm? 2. What is the surface area of a rectangular solid that is 9.2 cm by 7.5 cm by 2.7 cm? Check your answer with the answer key. If you get 8-10 Excellent! You may now proceed to the next lesson. 5-7 You need to review the processes you missed. 0-4 You need to repeat the whole process. Ask your teacher or elder to help you. 8

9 Key to Correction COMPREHENSION OF SURFACE AREA REVIEW 1) 60 dm 2 2) 24 dm 2 3) 119 cm 2 4) mm 2 5) 35 m 2 RY HESE A. 1) 38 cm 2 2) 76 cm 2 3) m 2 4) 262 dm 2 5) 262 m 2 B. Rectangular Prism Area of Each Face (m 2 ) otal Surface Length Width Height Front Back Left Right op Bottom Area 1) 9 m 4 m 7 m ) 3.4 m 1.6 m 7.2 m ) 10 m 4 m 8 m ) 7 m 8 m 12 m ) 5 m 11 m 9 m C. 1) G 2) R 3) E 4) A 5)! ON YOUR OWN A. 1) 392 dm 2 2) cm 2 3) 208 m 2 B. 1) 94 cm 2 2) 148 cm 2 3) 470 cm 2 4) 358 dm 2 5) 702 mm 2 C. 1) cm 2 2) cm 2 9