Answer:
- shaded: 45 units²
- non-shaded: 36 units²
- total area: 81 units²
Step-by-step explanation:
A "shaded area" problem can be worked by directly computing the area of the shaded shape, or by decomposing the figure in a convenient way. Here the overall square can be decomposed into unshaded triangles and a shaded square. The triangles have dimensions given, but the smaller square does not. Work must necessarily proceed from given dimensions to arrive at the values associated with dimensions not given.
For a problem like this, working the last question first can make it easier.
Total
The total area is the area of a square 6+3 = 9 units on a side. Its area is ...
Total area = s² = (9 units)² = 81 units²
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Non-shaded
The area of each of the four non-shaded triangles is ...
A = 1/2bh = 1/2(6 units)(3 units) = 9 units²
There are 4 triangles with that area that are not shaded, so ...
Non-shaded region = 4 × (9 units²) = 36 units²
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Shaded
The shaded region is that portion of the total area that is not Non-shaded. Its area will be the difference ...
Shaded area = Total area - Non-shaded area
Shaded area = 81 units² -36 units² = 45 units²
