Shape and Space – Area for 3D Shapes

3D Shapes:

Surface Area 

. The sum of all the areas of the faces in the shape

. A shape with three dimensions: length, width and height

1. Draw a sketch of the net of the shape (all the shapes that make up the shape)
2. Calculate the area of each shape and find the sum

Example 1:

Q) Workout the surface area of the cuboid

1. Draw a sketch of the net of the shape: Top = Bottom, Front = Back, Side = Side
2. Front → 2 x 5 = 10cm²

          Side → 10 x 5 = 50cm²

          Bottom → 10 x 2 = 20 cm²

3. Find total surface area → (10 x 2) + (50 x 2) + (20 x 2) = 160cm²

A) 160cm²

Example 2:

Q) Workout the surface area of the right-angle triangular prism

1. Draw a sketch of the net of the shape: both sides are equal
2. Front → 10 x 7 = 70cm²

          Side → ½ x 2 x 5 = 5cm²

          Back → 2 x 10 = 20 cm²

          Bottom → 10 x 5 = 50 cm²

3. Find total surface area → 70 + 20 + 50 + (5 x 2) = 150cm²

A) 150cm²