Surface Area
l=6, w=4, h=3
108
A box is twice as long as it is wide. Width = 4, height = 3 Find SA
Width = 4 → Length = 8, Height = 3
SA = 2(8×4) + 2(8×3) + 2(4×3) = 64 + 48 + 24 = 136
SA = 94 cm² l = 5, w = 3 Find h
94 = 2(5×3) + 2(5h) + 2(3h)
94 = 30 + 10h + 6h
94 = 30 + 16h
64 = 16h → h = 4
SA = 2(6×4) + (6×3) + (4×3) What mistake was made?
They didn’t multiply ALL terms by 2
(correct: each pair needs ×2)
l=8, w=5, h=2
132
A prism has a length of 12 cm. Width is half the length. Height is 5 cm. Find SA
Length = 12 → Width = 6, Height = 5
SA = 2(12×6) + 2(12×5) + 2(6×5) = 144 + 120 + 60 = 324
SA = 148 cm² l = 6, w = 4 Find h
148 = 2(6×4) + 2(6h) + 2(4h)
148 = 48 + 12h + 8h
148 = 48 + 20h
100 = 20h → h = 5
SA = 6×4 + 6×3 + 4×3 What is missing?
They are missing the ×2 for each face pair
(only added each face once)
l=10, w=7, h=3
242
A gift box is 10 inches tall. The length is 3 inches more than the width. Width is 5 inches. Find SA
Width = 5 → Length = 8, Height = 10
SA = 2(8×5) + 2(8×10) + 2(5×10) = 80 + 160 + 100 = 340
SA = 200 cm² l = 10, w = 5 Find h
200 = 2(10×5) + 2(10h) + 2(5h)
200 = 100 + 20h + 10h
200 = 100 + 30h
100 = 30h → h = 3⅓ (3.33)
Student forgot to multiply by 2. What should they have done?
They forgot to multiply by 2 for each pair of faces
l=12, w=9, h=4
384
A container is 20 cm long. The width is 4 cm less than the length. Height is 6 cm. Find SA
Length = 20 → Width = 16, Height = 6
SA = 2(20×16) + 2(20×6) + 2(16×6) = 640 + 240 + 192 = 1,072
SA = 312 cm² l = 12, w = 6 Find h
312 = 2(12×6) + 2(12h) + 2(6h)
312 = 144 + 24h + 12h
312 = 144 + 36h
168 = 36h → h = 4⅔ (4.67)
Student added dimensions instead of multiplying. Explain why this is wrong.
They added dimensions instead of multiplying to find area
(area requires multiplication, not addition)
l=15, w=6, h=5
390
A prism has width 8 cm. Height is 2 cm more than width. Length is double the height. Find SA
Width = 8 → Height = 10 → Length = 20
SA = 2(20×8) + 2(20×10) + 2(8×10) = 320 + 400 + 160 = 880
SA = 450 cm² l = 15, w = 10 Find h
450 = 2(15×10) + 2(15h) + 2(10h)
450 = 300 + 30h + 20h
450 = 300 + 50h
150 = 50h → h = 3
Student used volume formula instead. What is the correct formula?
They used volume (l×w×h)
Correct formula: SA = 2lw + 2lh + 2wh