Question 1199847: What is the area in the figure below, in m^2?
https://imgur.com/a/mBEHVsO Found 2 solutions by ikleyn, MathTherapy:Answer by ikleyn(52777) (Show Source):
The large triangle has the leg 7 meters and the hypotenuse 25 meters.
Hence, its other leg is = 24 meters.
The area of the large triangle is = 7*12 = 84 m^2.
The small triangle is similar to the large triangle with the similarity coefficient 4:7, or
(from the smaller to the larger).
Hence, the area of the smaller triangle is = = = 27 = 27.43 m^2 (rounded). ANSWER
What is the area in the figure below, in m^2?
https://imgur.com/a/mBEHVsO
You can use the fact that if the sides of similar triangles are in a certain ratio, then their areas'
ratio will be the SQUARED VALUES of that ratio.
Area of larger ΔABC = (AB)(AC) = (7)(24) = 7(12) = 84 m2.
So, shorter leg (ED) of smaller ΔCED to shorter leg of larger ΔABC results in a ratio.
Thus, the area of smaller ΔCED will be: OR
Larger ΔABC and smaller ΔCED (shaded) are SIMILAR.
Larger ΔABC boasts a 7-24-25 Pythagorean Triple, and AB and AC on larger ΔABC are 7 and 24 m, respectively.
Using triangular similarity (larger ΔABC to smaller ΔCED) theory to find segment EC on smaller ΔCED, we get:
7EC = 4(24) ---- Cross-multiplying
. With lengths of EC and ED (longer and shorter legs of ΔCED) being and 4,
we get:
