Solids

Exercise 1

Shown is a prism $A B C . D E F$ that has two square sides. These squares have edges of $4$ cm. Furthermore it is given that: $∠ B A C = 90 °$ , $B G = 1$ and $C H = 1$ .

a

Draw a life sized the cross-section of plane $G H D$ and the prism.

b

Calculate the size of the angles of triangle $G H D$ .

c

In the figure on the worksheet draw the cross-section of the plane $G H D$ with base plane $A B C$ .

Exercise 2

Of this eight sided figure $A B C D . E F G H$ the base $A B C D$ is a square of $4$ by $4$ , the height is $4$ and the top side $D E F G$ a square with diagonals of $2$ units. A horizontal cross-section has been drawn through the centers of all upright edges of this figure.

a

Make a life sized drawing of this cross-section. Show how you do this.

b

Calculate the total circumference of this cross-section.

Exercise 3

Draw on the worksheet the cross-section of the plane through $P$ , $Q$ and $C$ and the regular four-sided piramid $T . A B C D$ . Explain your construction.

Exercise 4

Draw on the worksheet the cross-section of the plane through $P$ , $Q$ and $R$ and the regular three-sided prism $A B C . D E F$ . Explain you construction.

Exercise 5

In the cuboid $A B C D . E F G H$ point $P$ lies exactly in the middle of $E F$ , and point $Q$ lies on $C G$ in such a way that $C Q : Q C = 2 : 1$ .

Draw on the worksheet the cross-section of the plane $A P Q$ and the bar. Explain your construction.

Exercises