Xyz and abc are similar triangles. given the dimensions shown in the diagram, what is the area of triangle abc ? express the answer in square units.

We know that

scale factor=XY/AB> 6/3> 2

area of a triangle=b*h/2
in the triangle XYZ
b=8.4 units
h=3.36 units
the area of triangle XYZ=8.4*3.36/2> 14.112 units²

in the triangle ABC
b=4.2 units
h=3.36/2> 1.68 units  (remember scale factor)
the area of triangle ABC=4.2*1.68/2> 3.528 units²

the answer is
the area of triangle ABC is 3.528 units²

alternative method

area triangle XYZ=area triangle ABC*[scale factor]²
area triangle ABC=area triangle XYZ/[scale factor]²> 14.112/2²---> 3.528 units²

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