Shapes From Squares Quiz / Test | For Children

Quiz Answer Key and Fun Facts

1. The shape you get if you join two identical squares beside each other has a name which is the same as a game that can be played using a marked set of playing pieces in this shape. What is its name?

Answer: Domino

A traditional set of domino tiles has 28 pieces, each divided into two squares, with different numbers of pips (spots) in each square. Seven of them have one half blank (counted as zero or as a wildcard, depending on what game you are playing) with 0, 1, 2, 3, 4, 5, or 6 pips in the other half. The set has every combination up to 6 pips in each half.

The word 'domino' comes from the name of a kind of hood originally worn by members of the clergy. It is not clear how the name got attached to the playing pieces; mathematicians use the word to describe any 2x1 rectangle that is being considered as two conjoined squares.

2. When three squares are joined together along their edges, they form a tromino. The three squares can be joined in a line, or in a bent shape like the one shown. The different shapes are often referred to by the name of a letter they resemble. Which of these might be used to describe the tromino in the picture?

Answer: V

This shape is also called the L shape. When it is in the position shown, it does look like an L; if you rotate it and stand it on its point, it looks more like a V. The tromino with three squares in a row is called the I shape. The word tromino was invented to combine the prefix tri- (for three) with the suffix -mino, as if the word domino were linguistically made up of di- (for two) and -mino.

3. These five shapes, called tetrominoes, are made by joining four squares along their edges. They are the playing pieces in a video game in which you try to make falling pieces fit together to fill the space at the bottom of the screen. What is its name?

Answer: Tetris

These are the only five shapes that can be made from four squares joined along their edges, but some of them look different when you flip them over. This can be useful when you are trying to cover a specific area with them. Rotating them, as can be done in the game 'Tetris', also helps to make them fit together neatly.

In 'Tetris', shapes fall one at a time, and the player moves them sideways and/or rotates them as they fall, so that they will land in the desired spot at the bottom. When a complete horizontal row is filled, all of those tiles disappear, and the stacks sink down one row. The aim is to clear enough rows to move on to the next level of the game before any of the stacks reaches the top of the screen.

4. Polyomino is the general term for all the shapes that can be made by connecting squares along their edges. This picture shows a polyomino sequence. How many squares will be in the next member of this sequence?

Answer: eight

The prefix poly- means many - a polygon is a shape with many corners formed by the straight lines that make up its sides; a polyomino has multiple squares joined together. They are usually named according to how many small squares have been joined together, using either Greek or Latin prefixes.

The polyominoes shown are L-shaped examples of a tromino (3 squares), a tetromino (4 squares), a pentomino (5 squares), a hexomino (6 squares), and a heptomino (7 squares). The next member of the sequence is an octomino, with 8 squares - 7 in a vertical line, and one attached to the right side of the top square.

5. This is an example of a pentomino, a shape with five squares joined together. Like many other sizes of polyomino, pentomino shapes are often identified by a letter that has a shape similar to the pentomino. Since they can be rotated and flipped over, some shapes can be made to resemble more than one letter. Which letter is NOT sometimes used to describe the pentomino in the picture?

Answer: x

This shape can also resemble a lower case d, as shown in the question. To get b, flip the d over sideways; to get p, rotate it halfway around so the tail is on the bottom left; to get q, flip the p sideways.

There are twelve different pentominoes, each described by one of the letters F, I, L, N, P (most common, because the upper case letter has the right shape, unlike B, D and Q), T, U (or C), V, W (or M), X, Y and Z. Personally, I think the F and the N really take some imagination!

6. These pictures show how combinations of nine different pentominoes can be fit together to make larger versions of each of the twelve pentomino shapes. If you were to join all twelve of the basic pentominoes together, how many squares would there be in the final shape?

Answer: 60

Since each pentomino covers five squares, when you put twelve of them together you will have 5x12, or 60, squares in your shape. A standard pentomino puzzle involves trying to make all twelve shapes fit onto a chessboard without any overlapping of pieces, or bits hanging out over the edge.

A game variant involves two players taking turns in placing a pentomino on a chessboard, with the winner the one who leaves no possible move for their opponent.

7. This shape has 54 small squares, arranged to make six large squares (each shown in a different color). It is special because you can fold it along the lines where large squares join and produce a familiar three-dimensional shape. What shape will it be?

Answer: Cube

A flat shape that can be folded to make a three-dimensional shape is called a net of the related solid figure. There are several hexominoes which are nets of a cube. You may have recognized the colors of a Rubik's cube, a popular puzzle invented in 1974 by the Hungarian architect Erno Rubik.

The challenge is to twist the cube in various ways so as to get all the squares of the same color together on one side of the cube.

8. This square is made up from nine small squares, all the same size, arranged in three rows of three squares.

Answer: True

When identical small squares are joined together to make a larger square, the number of squares in the large one is always the number you get if you multiply the number of small squares in each row by itself. This shape is called a 3x3 square, because it has three rows of three squares. We say that 9 is the square of 3. If you made 4x4 square, you would need 16 squares, and so on.

9. This square contains three sizes of square - one unit on a side (1x1 square), two units on a side (2x2 square) and three units on a side (3x3 square). Counting all three sizes of square, how many are there altogether?

Answer: 14

There are nine of the smallest size of square (1x1), and one of the largest size (3x3). You can also draw four 2x2 squares, one in each corner. Altogether, that makes 14 squares.

The next time someone asks you how many squares there are on a chessboard, you can either give the boring answer of 64 (8 rows of 8 squares), or you can consider all the possible sizes, as follows:
64 are 1x1
49 are 2x2
36 are 3x3
25 are 4x4
16 are 5x5
9 are 6x6
4 are 7x7
1 is 8x8
So the total is 204 squares of all sizes.

10. This square has been marked off into seven smaller shapes, which can be used to produce a variety of other figures. The first challenge usually posed is to provide the seven separate shapes, and ask to have them arranged into a square (without a handy diagram for guidance). The Chinese name for this set of shapes can be translated as "seven boards of skill". What is the common English name for them?

Answer: Tangram

The origin of the name tangram is unclear, but probably relates to the Chinese Tang dynasty. The puzzle was brought to the US from China by traders in the 19th century, and eventually spread through Europe. They were made from all sorts of materials, with varying degrees of value. Nowadays they are mostly mass-produced from plastic, and not often seen outside the mathematics classroom (where they are a useful tool in the exploration of geometry) unless as a children's toy.

Source: Author looney_tunes

This quiz was reviewed by FunTrivia editor NatalieW before going online.
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Shapes From Squares Trivia Quiz

Let's look at some interesting shapes you can make using squares.

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