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.

Accepted Solution

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