Solids

Exercise 1

Here you see a truncated cube with edges of $6$ cm. The points $P$ , $Q$ and $R$ are the centers of the edges they are situated on.

a

Draw a "parallel" projection of this truncated cube with an angle of $30 °$ and a scaling factor of $0,5$ .

b

Make a life-size drawing of ΔPQR at full scale.

c

The diagonal surface $D B Q S H$ is a pentagon. Make a life-size drawing of this diagonal surface of the truncated cube.

Exercise 2

Given is a regular pyramid $T . A B C D$ with the square $A B C D$ as the base. The edges of $A B C D$ are $6$ cm and the height $T S$ of the pyramid is $10$ cm. $S$ is the intersection point of $A C$ and $B D$ .

a

Draw a "parallel" projection of this pyramid on a grid.

b

Divide all edges into three equal parts. Explain what you do.

c

Connect the points in the base so that you get an octagon.

d

Is this octagon the base of a regular octagonal pyramid? Explain.

Exercise 3

When you connect the centers of the sides of a cube, you get an octahedron (regular eightsided polyhedron) $A B C D E F$ . In this octahedron $A C = B D = E F = 8$ cm.

a

Draw a parallel projection of this octahedron.

b

What shape do all sides of the octahedron have? Draw one of them full size.

c

What solid has vertices that are the centers of the sides of the octahedron?

Exercise 4

Here you see a so called hipped roof, a roof with a rectangular base $A B C D$ with the roof-ridge $E F$ situated exactly over the middle of the base. The roof itself consists of twee equilateral triangles and two symmetric trapeziums.

a

Draw a parallel projection of this roof in a grid with scale $1 : 100$ .

b

The roof itself consists of two isosceles triangles and two symmetric trapeziums. Use measurements in a suitable plane to determine the height of those two isosceles triangles. give your answer in whole dm. Draw one of those triangles on a scale of 1:100.

c

Determine the height of the two trapeziums by measuring in a suitable figure. Give the height in whole dm and draw one trapezium with scale 1:100.

Exercise 5

Beside you see a photo of the building "Willemswerf" in Rotterdam and below you see a view from above of a very simplified version of the building. This strongly simplified version has a height of $80$ m. The bend in the building starts $10$ m above the ground.

a

Draw your own parallel projection of the simplified version of the building "Willemswerf" in a grid with scale $1 : 100$ .

b

The bend in the building is trapezium shaped. Make a scaled drawing of that plane with scale $1 : 100$ .

Exercises