On the isometric grid
Draw cubes and cuboids on an isometric grid, one equal grid step at a time.
Questions in this lesson
Transcript
The cuboid below is drawn on isometric paper. Every step from one dot to the next dot along an edge is 1 unit, and the three hidden edges are drawn with dashes. How many unit cubes would it take to build this cuboid? Look at the corner right at the bottom of the drawing. That is the lowest corner, and 3 edges leave it: one going right and up, one going left and up, and one going straight up. The 3 edges drawn with dashes are behind the solid. They meet at the corner at the back, and no face you can see touches that corner. Start with the long edge, the one going right and up. It runs past 5 dots. The dots are not the units. The steps between them are. 5 dots in a row have only 4 steps between them. So the length is 4 units. Now the edge going left and up. It runs past 3 dots, and 3 dots have 2 steps between them. So the breadth is 2 units. And the edge going straight up. It runs past 4 dots, and 4 dots have 3 steps between them. So the height is 3 units. The cuboid is 4 steps long, 2 steps across and 3 steps high. Multiply the 3 counts: 4 times 2 times 3 is 24 unit cubes.
Your turn. Draw a cuboid 5 units by 2 units by 2 units on the isometric paper below. Every step from one dot to the next dot is 1 unit. Draw the hidden edges with dashes. Try it first. Pause if you like. Start at the lowest corner, near the bottom of the paper. Count 5 steps right and up. That edge is the length. Count 2 steps left and up. That edge is the breadth. Count 2 steps straight up. That edge is the height. The far end of each of those 3 edges is a corner next to the lowest one. Complete the solid: 6 more edges, and each one is parallel to an edge already drawn. That leaves the corner at the back. The 3 edges meeting there are behind the solid, so they are drawn with dashes. Drawn solid instead, those 3 edges would flatten the cuboid into a six-sided outline with 3 lines ruled across it. The lowest corner is where the 3 edges of a drawing start. A step from one dot to the next is 1 unit. The 3 dashed edges are the corner at the back.