Read top and front views

Separate a stack’s footprint from its height seen from the front.

Locate every stack

The drawing has five cubes in four stacks. The companion grid gives every stack’s height; 0 means an empty place. Its nearest corner is bottom right. The front arrow points along the viewing depth, from the bottom row toward the top row.

Front
Five cubes in four stacks.
201110000Front
Height at every place; 0 is empty.

Read two views of the same cubes

From above, each occupied place makes one square, whatever its height. From the front, stacks behind one another overlap. Use the greatest height at each left-to-right position: 2, 1, 1 here. The left heights 2 and 1 overlap; they do not add to 3. The bottom row is the ground.

Front
Top view: four occupied places.
Ground
Front view: heights 2, 1, 1.

Try a new stack

This new figure has four cubes in three stacks. Use the arrow to look from the front. At the leftmost position, compare the heights along the viewing depth.

Front
Four cubes in three stacks.
120100000Front
New height map; 0 is empty.

Try it

How high is the leftmost column in this new front view?

  1. 1 cube high.
  2. 2 cubes high.
Show the answer

1 cube high.

The two stacks at the left are each one cube high. They overlap when viewed from the front, so the greatest height stays 1. The middle column reaches 2.

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