Calculate surface area of rectangular prisms using painting project scenarios!
Scenario: You're helping paint a wooden storage box for the school. The box is a rectangular prism that's 2 meters long, 1.5 meters wide, and 1 meter tall. You need to know how much paint to buy by calculating the surface area (the total area of all the faces). Can you help calculate the surface area?
Surface area is the total area of all the faces (flat surfaces) of a 3D shape. It tells us how much surface the shape has on the outside. We measure surface area in square units like square meters (m²), square centimeters (cm²), or square feet (ft²).
Surface Area = Sum of all face areas
Add up the area of each face
How much wrapping paper you'd need to cover the shape
Painting walls, wrapping gifts, covering surfaces
A rectangular prism has 6 faces. Let's identify each face of our 2m × 1.5m × 1m storage box:
Front & Back: 2m × 1m = 2m² each
Length × Height
Left & Right: 1.5m × 1m = 1.5m² each
Width × Height
Top & Bottom: 2m × 1.5m = 3m² each
Length × Width
Total: 6 faces (2 front/back + 2 left/right + 2 top/bottom)
Let's calculate the surface area of our 2m × 1.5m × 1m storage box:
Front & Back: 2 × (2m × 1m) = 2 × 2m² = 4m²
Two identical faces
Left & Right: 2 × (1.5m × 1m) = 2 × 1.5m² = 3m²
Two identical faces
Top & Bottom: 2 × (2m × 1.5m) = 2 × 3m² = 6m²
Two identical faces
Total Surface Area = 4m² + 3m² + 6m² = 13m²
Add all face areas
Answer: 13 square meters
This is how much paint we need!
There's a faster way to calculate surface area using a formula:
Surface Area = 2(lw + lh + wh)
Where l = length, w = width, h = height
SA = 2(2×1.5 + 2×1 + 1.5×1)
Substitute our values
SA = 2(3 + 2 + 1.5) = 2(6.5) = 13m²
Calculate step by step
Same answer: 13 square meters! Both methods work.
A gift box is 3cm long, 2cm wide, and 4cm tall. What is its surface area?
SA = 2(3×2 + 3×4 + 2×4) = 2(6 + 12 + 8) = 2(26) = 52cm²
Using the formula method
Answer: 52 square centimeters
A classroom storage cabinet is 1.2m long, 0.8m wide, and 2m tall. How much paint is needed to cover all surfaces?
SA = 2(1.2×0.8 + 1.2×2 + 0.8×2) = 2(0.96 + 2.4 + 1.6) = 2(4.96) = 9.92m²
Calculate surface area
Answer: 9.92 square meters of paint needed