Complementary Area?

Geometry Level 2

The diagram above shows two congruent right triangles 12-16-20 overlapping to form a dark blue region.

Find the area of this dark blue region.

1 solution

Abhay Tiwari
Apr 25, 2016

If we see, The $\triangle AFC$ $\sim$ $\triangle ADE$ by $AAA$ property.

Now: we know that $AC=12$

$\frac{AC}{AE}=\frac{FC}{DE}$

On solving this we get: $FC=9$

Area= $\frac{1}{2}*AC*FC$

Area= $\frac{1}{2}*12*9=\boxed{54}$

Thank you for your solution.

Fun fact : 12-16-20 is the smallest Pythagoras triplets that gives an integer solution.

Chung Kevin - 5 years, 1 month ago

Ok great, was not known to this fact, thanks a lot!

Abhay Tiwari - 5 years, 1 month ago

Sir, please have a look at this if there is some ambiguity, then please tell me.

Abhay Tiwari - 5 years, 1 month ago