his star is made up of 4 equilateral triangles of equal area and a square.Question promptIf the area of the shaded region is 9 cm2square centimetres, what is the perimeter of the star?Question response areaSelect one option12 cm24 cm30 cm36 cm

To solve this problem, we first need to understand the geometry of the star. The star is made up of 4 equilateral triangles and a square. The area of the shaded region is given as 9 cm².

1. Since the area of the shaded region is the area of the square, we can find the side length of the square. The formula for the area of a square is side². So, side = sqrt(area) = sqrt(9) = 3 cm.

2. The side length of the square is also the side length of each equilateral triangle. The perimeter of an equilateral triangle is 3 times the length of one side. So, the perimeter of one triangle is 3 * 3 = 9 cm.

3. Since there are 4 triangles, the total perimeter of the triangles is 4 * 9 = 36 cm.

4. However, each side of the square is shared by two triangles, so we have double-counted these sides in our perimeter calculation. There are 4 sides to the square, so we need to subtract 4 * 3 = 12 cm from our total.

5. Therefore, the perimeter of the star is 36 - 12 = 24 cm.

So, the correct answer is 24 cm.