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

646464888121212222333 What is the area of the blue polygon, given that the two polygons are similar and the area of the green polygon is 64?

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Step-by-step video solution

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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

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1

Understand the problem

646464888121212222333 What is the area of the blue polygon, given that the two polygons are similar and the area of the green polygon is 64?

2

Step-by-step solution

From the similarity, it follows that:

123=4 \frac{12}{3}=4

Therefore:

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

6416=S \frac{64}{16}=S

S=4 S=4

3

Final Answer

4

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