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12345Projections

Solutions to the exercises

Exercise 1
a

See the figure.

b

P Q R becomes an equilateral triangle with edges of 4,2 cm.

c

First draw rectangle D B F H with D B = H F 8,5 and D H = B F = 6 cm.
Next you draw the center Q of B F and point S in such a way that F S = 1 4 H F .
Now you can draw pentagon D B Q S H .

Exercise 2
a

See the figure.

b

See figure at a. Just divide each edge into three by measurement. This is allowed because the figure is a parallel projection.

c

See figure at a.

d

No, the base is not an octagon with equal edges. There are edges of 2 cm and edges of 2 2 2,8 cm.

Exercise 3
a

See the figure.

b

They are equilateral triangles with edges of approximately 4 2 5,7 cm.

c

A cube.

Exercise 4
a

Let it be checked, when in doubt.

b

Both triangles have a base of 8 cm and a height of approximately 5,8 cm.
That height is the line segment from F to the center N of B C of the line segment from E to the center M of A D . When you draw E M N F full scale you can measure those heights.

c

The height of a trapezium is approximately 6,4 cm.
You measure that height in a triangle through E or F and parallel to B C .

Exercise 5
a

See the figure.

b

See the trapezium below.

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