Similar Polygons Area Problem: Finding Blue Triangle Area Given Green Area of 64

Question

What is the area of the blue polygon, given that the two polygons are similar and the area of the green polygon is 64?

00:00 Find the area of the polygon

00:03 The polygons are similar according to the given

00:07 We want to find the similarity ratio

00:11 We'll break down 12 into factors (3) and (4) and reduce

00:14 This is the similarity ratio

00:18 The similarity ratio squared equals the area ratio squared

00:34 We'll substitute appropriate values and solve to find the area of polygon 2

00:39 We'll multiply by the reciprocal to isolate the area

00:53 And this is the solution to the question

From the similarity, it follows that:

$\frac{12}{3}=4$

Therefore:

$\frac{64}{S}=16$

$\frac{64}{16}=S$

$S=4$