Question

find the surface area of each rectangular prism.

1. 9 mm 3 mm 13 mm surface area =
2. 20 cm 6 cm 4 cm surface area =
3. 16 m 5 m 14 m surface area =
4. 17 ft 4 ft 14 ft surface area =
5. 13 in 19 in 4 in surface area =
6. 14 mm 9 mm 3 mm surface area =
7. 12 cm 2 cm 7 cm surface area =
8. 6 in 13 in 4 in surface area =
9. 8 ft 15 ft 4 ft surface area =
10. a gift - box in the shape of a rectangular prism has 20 centimeters length, 14 centimeters width and 10 centimeters height. how much the paper will you need to wrap the gift box? surface area =

Answer:

1. Recall the surface - area formula for a rectangular prism:

• The formula for the surface area \(SA\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(SA = 2(lw+lh + wh)\).

1. For the first rectangular prism (\(l = 13\) mm, \(w = 9\) mm, \(h = 3\) mm):

• Step1: Calculate \(lw\).
• \(lw=13\times9 = 117\) \(mm^{2}\).
• Step2: Calculate \(lh\).
• \(lh = 13\times3=39\) \(mm^{2}\).
• Step3: Calculate \(wh\).
• \(wh=9\times3 = 27\) \(mm^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(117 + 39+27)=2\times183 = 366\) \(mm^{2}\).

1. For the second rectangular prism (\(l = 20\) cm, \(w = 4\) cm, \(h = 6\) cm):

• Step1: Calculate \(lw\).
• \(lw=20\times4 = 80\) \(cm^{2}\).
• Step2: Calculate \(lh\).
• \(lh=20\times6 = 120\) \(cm^{2}\).
• Step3: Calculate \(wh\).
• \(wh=4\times6=24\) \(cm^{2}\).
• Step4: Calculate the surface area.
• \(SA = 2(80 + 120+24)=2\times224 = 448\) \(cm^{2}\).

1. For the third rectangular prism (\(l = 16\) m, \(w = 5\) m, \(h = 14\) m):

• Step1: Calculate \(lw\).
• \(lw=16\times5 = 80\) \(m^{2}\).
• Step2: Calculate \(lh\).
• \(lh=16\times14 = 224\) \(m^{2}\).
• Step3: Calculate \(wh\).
• \(wh=5\times14 = 70\) \(m^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(80 + 224+70)=2\times374=748\) \(m^{2}\).

1. For the fourth rectangular prism (\(l = 17\) ft, \(w = 4\) ft, \(h = 14\) ft):

• Step1: Calculate \(lw\).
• \(lw=17\times4 = 68\) \(ft^{2}\).
• Step2: Calculate \(lh\).
• \(lh=17\times14 = 238\) \(ft^{2}\).
• Step3: Calculate \(wh\).
• \(wh=4\times14 = 56\) \(ft^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(68 + 238+56)=2\times362 = 724\) \(ft^{2}\).

1. For the fifth rectangular prism (\(l = 13\) in, \(w = 19\) in, \(h = 4\) in):

• Step1: Calculate \(lw\).
• \(lw=13\times19 = 247\) \(in^{2}\).
• Step2: Calculate \(lh\).
• \(lh=13\times4 = 52\) \(in^{2}\).
• Step3: Calculate \(wh\).
• \(wh=19\times4 = 76\) \(in^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(247+52 + 76)=2\times375 = 750\) \(in^{2}\).

1. For the sixth rectangular prism (\(l = 14\) mm, \(w = 9\) mm, \(h = 3\) mm):

• Step1: Calculate \(lw\).
• \(lw=14\times9 = 126\) \(mm^{2}\).
• Step2: Calculate \(lh\).
• \(lh=14\times3 = 42\) \(mm^{2}\).
• Step3: Calculate \(wh\).
• \(wh=9\times3 = 27\) \(mm^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(126 + 42+27)=2\times195 = 390\) \(mm^{2}\).

1. For the seventh rectangular prism (\(l = 12\) cm, \(w = 2\) cm, \(h = 7\) cm):

• Step1: Calculate \(lw\).
• \(lw=12\times2 = 24\) \(cm^{2}\).
• Step2: Calculate \(lh\).
• \(lh=12\times7 = 84\) \(cm^{2}\).
• Step3: Calculate \(wh\).
• \(wh=2\times7 = 14\) \(cm^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(24 + 84+14)=2\times122 = 244\) \(cm^{2}\).

1. For the eighth rectangular prism (\(l = 13\) in, \(w = 6\) in, \(h = 4\) in):

• Step1: Calculate \(lw\).
• \(lw=13\times6 = 78\) \(in^{2}\).
• Step2: Calculate \(lh\).
• \(lh=13\times4 = 52\) \(in^{2}\).
• Step3: Calculate \(wh\).
• \(wh=6\times4 = 24\) \(in^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(78 + 52+24)=2\times154 = 308\) \(in^{2}\).

1. For the ninth rectangular prism (\(l = 8\) ft, \(w = 4\) ft, \(h = 15\) ft):

• Step1: Calculate \(lw\).
• \(lw=8\times4 = 32\) \(ft^{2}\).
• Step2: Calculate \(lh\).
• \(lh=8\times15 = 120\) \(ft^{2}\).
• Step3: Calculate \(wh\).
• \(wh=4\times15 = 60\) \(ft^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(32 + 120+60)=2\times212 = 424\) \(ft^{2}\).

1. For the tenth rectangular prism (\(l = 20\) cm, \(w = 14\) cm, \(h = 10\) cm):

• Step1: Calculate \(lw\).
• \(lw=20\times14 = 280\) \(cm^{2}\).
• Step2: Calculate \(lh\).
• \(lh=20\times10 = 200\) \(cm^{2}\).
• Step3: Calculate \(wh\).
• \(wh=14\times10 = 140\) \(cm^{2}\).
• Step4: Calculate the surface area.
• \(SA=2(280 + 200+140)=2\times620 = 1240\) \(cm^{2}\).

1. Surface Area = 366 \(mm^{2}\)
2. Surface Area = 448 \(cm^{2}\)
3. Surface Area = 748 \(m^{2}\)
4. Surface Area = 724 \(ft^{2}\)
5. Surface Area = 750 \(in^{2}\)
6. Surface Area = 390 \(mm^{2}\)
7. Surface Area = 244 \(cm^{2}\)
8. Surface Area = 308 \(in^{2}\)
9. Surface Area = 424 \(ft^{2}\)
10. Surface Area = 1240 \(cm^{2}\)