4.4 Question 14

LauraKathleen 9-05

" Eliza is building a model of the canvas tent her family uses in Behchoko, NWT. The model will have a peak height of 12 cm. The actual tent floor measures 2.4 m by 3 m. The walls are 1.5 m high and the peak height is 2.4 m.

a) What scale factor will Eliza need to use for her model?

b) The front of the tent is a pentagon. Calculate the dimensions of this polygon on the model.

c) Calculate the other dimensions of the tent model. "

It's always smart to highlight or underline the key points in a question :)

a) To find the scale factor, divide the actual by the reduction. Here's a picture to help:





Step 1: Convert

2.4 m X 100 = 240 cm.

240 cm/ 12 cm = 20 cm

The scale factor for this problem is 20 cm.

b) It gives the bottom length of the pentagon, so naturally, it's the easiest to calculate.

Solution:

3 m/ 100 = 300 cm

300 cm/20 = 15 cm (Divide by 20 because that is the scale factor)

The rest of the sides of the pentagon are the same length, so if you can figure out one, you have them all! For this one, use the Pythagorean Theory.
(a squared + b squared = c squared)






a squared + b squared = c squared

1.5 X 1.5 + 0.9 X 0.9 = c squared

2.25 + 0.81 = c squared

3.06 = c

square root of 3.06 = 1.75 (approx.)

1.75/ 20 = 0.0875 (Divide by 20 because 20 is the scale factor)

0.0875 X 100 = 8.75 cm




Sorry if this is wrong! Please correct me! THANKS :D

Brianna! It's your turn next!

MERRY CHRISTMAS