can consider it a notable achievement. It isn't exactly the beall, endall of mathematical accomplishments but it is quite a fundamental standard
by which anyone's quantitative literacy is
benchmarked
benchmark (v.): benchmark
test or evaluate performance for purposes of establishing a comparative score

(even outside of or beyond this course). With this said, let's move on to one last yet more
elaborate
elaborate (adj.): Elabbohrruht
marked by complexity and richness of detail; developed or executed with care and in minute detail; intricate or fancy

example where several of our ideas combine in order to solve a problem involving what's commonly known as a
composite figure.
* * *_{ }
Example 5
Find the Area, in hectares (ha), for the property shown in the illustration.
Hint: use the equivalence that 1 ha = 10,000 m².
The first realization that needs to occur is that the property consists of two simple figures, a trapezoid
(on the left) and a right triangle (on the right). With this in mind, one may proceed to find the Area of each piece
separately and then add them together to find the total Area of the entire figure / property. The length of the dashed


vertical line ( i.e., the height of the right triangle) is unknown, which is also a key dimension to the trapezoid.
Thus, the first calculation will be to determine this quantity (as it is needed in order for us to obtain the Area for either of the two simple figures) via
Pythagoras:

Pythagoras of Samos
A somewhat mysterious Greek mathematician, who lived circa 500 B.C.E., and whose name is accredited to the infamous Pythagorean Theorem
(a² + b² = c²).

h 
² 
+ 
( 
300 m 
) 
² 
= 
( 
500 m 
) 
² 

h 
² 
+ 
90,000 m² 
= 
250,000 m² 


h 
² 
= 
250,000 m² 
 
90,000 m² 

h 
² 
= 
160,000 m² 

h 
= 
√160,000 m² 

h 
= 
400 m 

And the picture now looks like...
