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Surface area of prisms

Find the surface area of rectangular and triangular prisms by summing the areas of all faces.

Worked examples

Surface area of a rectangular prism

Straightforward

Problem

A rectangular prism has length 7 cm7 \text{ cm}, width 4 cm4 \text{ cm} and height 3 cm3 \text{ cm}. Find its surface area.

Surface area of a triangular prism

Moderate

Problem

A triangular prism has a right-angled triangular cross-section with legs 5 cm5 \text{ cm} and 12 cm12 \text{ cm}. The length of the prism is 6 cm6 \text{ cm}. Find the total surface area.

Surface area of an open-top rectangular tray

Challenging

Problem

A rectangular storage tray has length 40 cm40 \text{ cm}, width 25 cm25 \text{ cm} and height 15 cm15 \text{ cm}, and has no lid. Find the total surface area of the tray.

Practise

Q1·Straightforward
A rectangular prism has length 5 cm5 \text{ cm}, width 3 cm3 \text{ cm} and height 2 cm2 \text{ cm}. Find its surface area in cm2\text{cm}^2.
Q2·Straightforward
A rectangular prism has length 6 cm6 \text{ cm}, width 4 cm4 \text{ cm} and height 3 cm3 \text{ cm}. Find its surface area in cm2\text{cm}^2.
Q3·Straightforward
A rectangular prism has length 8 cm8 \text{ cm}, width 5 cm5 \text{ cm} and height 2 cm2 \text{ cm}. Find its surface area in cm2\text{cm}^2.
Q4·Straightforward
A rectangular prism has length 10 cm10 \text{ cm}, width 3 cm3 \text{ cm} and height 4 cm4 \text{ cm}. Find its surface area in cm2\text{cm}^2.
Q5·Moderate
A triangular prism has a right-angled triangular cross-section with legs 3 cm3 \text{ cm} and 4 cm4 \text{ cm}. The length of the prism is 9 cm9 \text{ cm}. Find the total surface area in cm2\text{cm}^2.
Q6·Moderate
A triangular prism has a right-angled triangular cross-section with legs 5 cm5 \text{ cm} and 12 cm12 \text{ cm}. The length of the prism is 8 cm8 \text{ cm}. Find the total surface area in cm2\text{cm}^2.
Q7·Moderate
A triangular prism has a right-angled triangular cross-section with legs 6 cm6 \text{ cm} and 8 cm8 \text{ cm}. The length of the prism is 7 cm7 \text{ cm}. Find the total surface area in cm2\text{cm}^2.
Q8·Moderate
A triangular prism has a right-angled triangular cross-section with legs 9 cm9 \text{ cm} and 12 cm12 \text{ cm}. The length of the prism is 5 cm5 \text{ cm}. Find the total surface area in cm2\text{cm}^2.
Q9·Challenging
A rectangular storage box has no lid. It has length 50 cm50 \text{ cm}, width 30 cm30 \text{ cm} and height 20 cm20 \text{ cm}. Find the total surface area of the box (excluding the open top) in cm2\text{cm}^2.
Q10·Challenging
A rectangular gift box has length 25 cm25 \text{ cm}, width 20 cm20 \text{ cm} and height 10 cm10 \text{ cm}. How many cm2\text{cm}^2 of wrapping paper are needed to cover the outside of the box exactly?
Q11·Challenging
A wooden ramp is shaped like a triangular prism. Its cross-section is a right-angled triangle with base 60 cm60 \text{ cm} and perpendicular height 45 cm45 \text{ cm}. The ramp is 80 cm80 \text{ cm} wide. Find the total surface area of the ramp in cm2\text{cm}^2.
Q12·Challenging
A rectangular room has length 4 m4 \text{ m}, width 3 m3 \text{ m} and wall height 2.5 m2.5 \text{ m}. Tiles cost $35\$35 per m2\text{m}^2. The floor and all four walls are tiled. Find the total cost in dollars.