In order to solve this problem, I would approach it in three steps:
1. First, calculate the area of the triangles drawn inside the polygon. It looks like each of the triangles has a base length of 6cm and a height of 8cm. The formula for the area of a triangle is 1/2×b×h.
Using this formula, we can calculate the area for one triangle to be:
1/2 × 6 × 8 = 24cm²
We also have a total of 8 triangles that each have the same base and height lengths, so we can find the total area that the triangles occupy by multiplying the area (24cm²) by 8.
So, the total area occupied by the triangles is:
8 × 24 = 192cm²
2. Second, we can calculate the area of the square inside the polygon. The formula for the area of a square is b*h. Our square has a base length of 12cm and a height of 12cm.
Using our formula, we can calculate the area of the square as:
12 × 12 = 144cm²
3. Our last step is to add our total areas together. This will give us the area of the whole shape.
192cm² + 144cm² = 336cm²
<em>Our final area for the polygon is 336cm².</em>
