Promoting the study of Geometry
Joining forces with institut-delbol.com, mouctar.org is publishing the first challenge.
The callenge second part is now solved. No more answers will be accepted. There was no winner for this challenge.
The following is the Algebraic method.
PROBLEM 2: THE TRAPEZOID
An agency is assigning the area bounded by figure to a city population.
Each member will receive an equal area of a land plot.
Calculations have shown that out of the 5160 members of the population, 2000 will receive their plots from the area covered by triangle
The remaining people will be assigned plots from , (See graph).
and
1. Find the area of
2. Verify the area of ADC using the Heron’s Formula
3. What is the area, in square meters, assigned to each person?
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SOLUTION: METHOD BY ALGEBRA
Let
From the right triangle We have the hypothenuse .
We have:
We also have the right triangle
Another equality:
We can then say:
The area of contains 3160 plots of land out of 5160.
For :
The area of the
OR
Area
Area
Now let’s look for the total area:
Area
Area :
Area
We plugin:
Area
Area
For :
The area of the
OR
Area
Area
TOTAL AREA :
Area
We plugin:
Area
Area
Comparing Areas:
Area
Area
This yields:
OR
We simplify:
We plugin:
We can write, for simplicity:
We divide both sides by
By moving we get:
Multiply both sides by 2:
We can also write:
Let
We get:
Let’s square both sides:
We plugin the values:
Rounded Value here:
Areas:
The other sides:
Area
Area
Area
Rounding:
Area
Trapezoid:
Using the heron Formula for Area ADC
The sides are: , ,
Calculating :
Area
Area
ROUNDING:
Area
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