Key points
The areaA measure of the size of any plane surface or 2D shape. Area is measured in square units, for example, square centimetres or square metres: cm虏 or m虏. is the total area of all the faceOne of the flat surfaces of a solid shape. of the shape. For example, the surface area of a cube is the total area of all six square faces. This is 6 脳 side虏.
Surface area is measured in square units including cm虏 and m虏.
The edgeThe line formed by joining two vertices of a shape. The line formed when two faces meet. of the square is the edge of the cube and is the length, width and height dimensions of the 3D shape.
A cuboidA 3D shape with six rectangular faces. The opposite faces are congruent. has six faces and opposite pairs of faces are congruentShapes that are the same shape and size, they are identical.. The dimensionThe length, width, height or depth of something. of a cuboid are paired to give three congruent pairs of faces. For example, a cuboid with dimensions 2 cm 脳 3 cm 脳 4 cm has two faces which measure 2 cm 脳 3 cm, two which measure 2 cm 脳 4 cm and two which measure 3 cm 脳 4 cm.
The netA group of joined 2D shapes which fold to form a 3D shape. of a 3D shape is what a shape looks like when it is opened out into a 2D shape. The net can help to show the areas of each face that make up the surface area of a shape.
Calculating the surface area of a cube
A cube has six congruent square faces. The total area of the faces is the surface area of the cube.
To work out the surface area of a cube:
- square (verb)Multiply a number by itself. one edge of the cube. This gives the area of one square face.
- Multiply the area of one square face by six.
To find the length of an edge of a cube:
- Divide the total surface area by six. This gives the area of one square face.
- Find the square root 鈭A value that, when multiplied by itself, gives the number. Eg, 4 脳 4 = 16, so the square root of 16 is 4. 鈭16 = 4.
Examples
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Question
What is the total surface area of a cube with an edge of 11 mm?
The surface area of a cube is 6 脳 area of a square face = 6 脳 edge虏
6 脳 11虏 = 726
The surface area of the cube is 726 mm虏.
Calculating the surface area of a cuboid
A cuboid has three pairs of congruentShapes that are the same shape and size, they are identical. faces:
- The top face and the base face.
- The left and right faces.
- The front and back faces.
To work out the total surface area of a cuboid:
- Find the area of the top and base faces. This is length 脳 width 脳 2
- Find the area of the right and left faces. This is width 脳 height 脳 2
- Find the area of the front and back faces. This is length 脳 height 脳 2
- Add the face areas to find the total surface area.
The formula for the surface area of a cuboid with the dimensions 饾拲 脳 饾挊 脳 饾拤 can be given as:
Surface area = 2饾拲饾挊 + 2饾挊饾拤 + 2饾拲饾拤 or surface area = 2(饾拲饾挊 + 饾挊饾拤 + 饾拲饾拤).
Examples
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Question
Find the total surface area of the cuboid.
The dimensions of the cuboid are length 12 cm, width 3 cm and height 7 cm.
Work out the area of the top and base faces (length 脳 width 脳 2).
12 脳 3 脳 2 = 72. The area of the top and base faces is 72 cm虏.
Work out the area of the right and left faces (width 脳 height 脳 2).
3 脳 7 脳 2 = 42
The area of the left and right faces is 42 cm虏.
Work out the area of the front and back faces (length 脳 height 脳 2).
12 脳 7 脳 2 = 168
The area of the front and back faces is 168 cm虏.
Find the total of the areas of all faces.
72 + 42 + 168 = 282
The total surface area of the cuboid is 282 cm虏.
Practise finding the surface area
Practise finding the surface area of cubes and cuboids with this quiz. You may need a pen and paper to help you with your answers.
Quiz
Game - Divided Islands
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