Geometry In Design - McGraw-Hill Ryerson

Example 2 Design a Pentagonal House
An architect has designed a house in the shape of a regular pentagonal
prism. The floor forms a pentagon with a side length of 6 m. The five
walls are congruent squares. The peaked roof is made of five congruent
equilateral triangles. Select a suitable scale. Draw a net that can be used to
make a scale model of this house. Then, cut out your net and fold it into a
model of the house. Tape the model together.
Solution
Method 1: Use Pencil and Paper
• Choose an appropriate scale. For example, 1 cm represents 1 m. Draw
a regular pentagon. A regular pentagon consists of five congruent
isosceles triangles whose apexes meet at the centre of the pentagon.
The apex angle for each triangle is 360° ÷ 5 = 72°. Draw a dot for the
centre, and a horizontal line segment to the first vertex. Draw an angle
of 72° from the horizontal line segment. Use compasses to help you
create an isosceles triangle that includes the second vertex. Continue
this process until you have 5 vertices. Join the vertices.
• Use a ruler and compasses to draw a square on each side of the
pentagon. Then, draw an equilateral triangle on each square.
• Use your net to make a
scale model of the house.
Method 2: Use The Geometer’s Sketchpad®
• Draw the pentagonal base. Turn on automatic labelling of points. Sketch
a horizontal line segment AB. Select point A, and choose Mark Center
from the Transform menu. Select the segment and point B. Choose
Rotate from the Transform menu. Change the fixed angle to 72°.
Select Rotate. Continue until you have five vertices. Join the vertices.
• Draw the square walls. Select one endpoint of a side. Choose Mark
Center from the Transform menu. Select the segment and the other
endpoint. Choose Rotate from the Transform menu. Change the fixed
angle to 90°. Select Rotate. Repeat for each side. Then, use the other
6.4 Scale Models • MHR 39