Areas for non-similar figures

Is it possible to have a relationship where the ratio of the Lengths is equal to the ratio of the Areas, i.e.,
Mathsymbol_lengths_w_areas.jpg ?

Look at the triangles below:
triangles.jpg
Do Triangles ACD and ABC have in common? Do they share a common height? [Are you able to locate this common height?]




Example 1:

Look at the diagram below:
Triangle ABC shares the same height with Triangles ACD (or Triangle ABD).

triangles2.jpg
Find the ratio of BC: CD
=
5 : 3

Find the ratio of Area BCA: Area CDA
=
0.5*5*2 : 0.5*3*2

=
5 : 3 [Do you know how to get this?]
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PAUSE --- Still Confused? Look at the video below:

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Question 1:

Look at the diagram below:
Triangle4.jpg
Find the Area of Triangle ABC: Area of Triangle ACD.
[**Questions: Do I need to find the actual areas for the 2 triangles? Do I need to know the perpendicular height for both the triangles?]


Question 2:

Look at the diagram below:
Figure5.jpg
Given that ABCD is a paralleogram and area of triangle CEF : area of triange ADE = 1 : 9
Find the ratio of Area triangle CEF: Area of parallelogram ABCD?

[Answer: 1 : 24 ] --- Are you able to derive to this answer?
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homework_title.gif
Homework (to be submitted in hardcopy)
Please download the Worksheet and Assignment.


For Mr Colin Toh's classes, please use this:


Complete both the work by Week 4, Monday [18 July 2011]