Question 1

Tessa is a student in a woodwork class.

The class will construct geometrical solids from a block of wood.

Tessa has a piece of wood in the shape of a rectangular prism.

This prism, , shown in Figure 1, has base length 24 cm, base width 28 cm and height 32 cm.

On the front face of Figure 1, , Tessa marks point halfway between and as shown in Figure 2 below. She then draws line segments and as shown.

1. Determine the length, in cm, of .  (1 mark)
2. Calculate the angle . Write your answer in degrees, correct to one decimal place.  (1 mark)
3. Calculate the angle correct to one decimal place.  (1 mark)
4. What fraction of the area of the rectangle does the area of the triangle represent?  (1 mark)

Question 2

Tessa carves a triangular prism from her block of wood.

Using point , halfway between and on the back face, , of Figure 1, she constructs the triangular prism shown in Figure 3.

1. Show that, correct to the nearest centimetre, length is 34 cm.  (1 mark)
2. Using length as 34 cm, find the total surface area, in cm², of the triangular prism in Figure 3.  (2 marks)

Question 3

Tessa's next task is to carve the right rectangular pyramid shown in Figure 4 below.

She marks a new point, , halfway between points and in Figure 3. She uses point to construct this pyramid.

1. Calculate the volume, in cm³, of the pyramid in Figure 4.  (1 mark)
2. Show that, correct to the nearest cm, length is 37 cm.  (2 marks)
3. Using as 37 cm, demonstrate the use of Heron's formula to calculate the area, in cm², of the triangular face .  (2 marks)