Unit 7 Section 1 : Shapes

You should be familiar with the common 2-D shapes, but to recap, we give the names and definitions below.

Example 1

What could each one of the following shapes be if it has 4 sides and:

(a) opposite sides equal and parallel,
It could be a parallelogram, rhombus, rectangle or square.
(b) all sides equal,
It could be a rhombus or square.
(c) two adjacent angles are right angles?
It could be a trapezium, rectangle or square.

Example 2

For the grid opposite, name all shapes that are:

(a)

congruent,

Congruent to A means the same size and shape as A. The shapes congruent to A are G, L and K.
(b)

similar to shape A.

Similar to A means the same shape as A but not necessarily the same size as A. The shapes similar to A are C, F, G, J, K and L.

Example 3

Using 20 m of fencing, design four different rectangular enclosures. For each one, find its area. Which shape gives the maximum area?

Possible shapes could be:
area = 2 × 8 = 16m²
area = 3 × 7 = 21m²
area = 4 × 6 = 24m²
area = 5 × 5 = 25m²
The square (5 m × 5 m) gives the maximum area.

Exercises

Question 1

What could each one of the following shapes be if it has 4 sides and:

(a)

all angles are right angles,

(b)

only one pair of opposite sides are parallel, but not equal,

(c)

diagonals intersect at right angles?

Question 2

Which of the shapes in the diagram below are:

(a) congruent, (b) similar

to shape A ?

List the numbers separated by commas: e.g. A, B, C, D
(a)
(b)
Question 3

Using 40 cm of wire, design different rectangles. For each one, find its area.
What shape gives the maximum area?

The shape that gives the maximum area is a of side cm.
Question 4

These two congruent triangles make a parallelogram.

(a)
On the grid below, draw another congruent triangle to make a rectangle.
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(b)
On a copy of the grid below, draw another congruent triangle to make a bigger triangle.
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(c)
On a copy of the grid below, draw another congruent triangle to make a different bigger triangle.
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Question 5

Mike has a triangle grid. He shades in 2 triangles to make a shape with 4 sides.

(a)
Shade in 2 triangles on a grid below to make a different shape with 4 sides.
(b)
On another grid, shade in 2 triangles to make another different shape with 4 sides.
(c)
On another grid, shade in 4 small triangles to make a bigger triangle.
(d)
On the grid below, shade in more than 4 small triangles to make a bigger triangle.
Question 6
(a)

Scott has 9 small square tiles. On the following grid, show how Scott can make a square in the same way with 9 small square tiles.

(b)

On another grid, show how to make a square with more than 9 of these small square tiles.

How many tiles are there in your square?

(c)

Huw wants to make some more squares with the tiles. Write down 3 other numbers of tiles that he can use to make squares.

Question 7

Helen has these eight rods.

She can use 5 of her rods to make a rectangle.

This combination is:5,5,8,6 + 2
(a)

On a copy of the grid above, show how to make a different rectangle with a different shape with 5 of Helen's rods.

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(b)

On a larger grid, 13 squares by 10 squares, show how to make a rectangle with 6 of Helen's rods.

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(c)

On another large grid, show how to make a square with all 8 of Helen's rods.

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