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A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.

How many triangles are needed to compose a region that is LaTeX: 1\frac{1}{2}1 1 2 square meters?"

User Lxgr
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1 Answer

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Final answer:

To compose a region of 1½ square meters, we need 54 identical triangles, assuming each triangle comes from a square meter divided into 9 smaller squares, further decomposed into triangles.

Step-by-step explanation:

The student's question involves decomposing a square and working with areas and triangles, which falls under the subject of Mathematics. Specifically, this is a geometry problem often encountered at the middle school level. Let's start by understanding the first part of the problem. A square with an area of 1 square meter is divided into 9 identical smaller squares. This means that each smaller square has an area of \( \frac{1}{9} \) square meter. When each small square is divided into two identical triangles, each triangle will have an area of \( \frac{1}{18} \) square meter.

To find out how many of these triangles are needed to compose a region of \(1\frac{1}{2}\) square meters, we perform the following calculation:

\(1\frac{1}{2} \) square meters \( = \frac{3}{2} = \) total area in square meters
\( \frac{3}{2} \div \frac{1}{18} = 3 \times 18 = 54 \) triangles needed

Therefore, we need 54 triangles to compose a region of \(1\frac{1}{2}\) square meters.

User Mahabub Islam Prio
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