Final answer:
To find the perimeter of the cross-shaped pattern, first find the dimensions of the rectangle. Then calculate the area of the rectangle and divide it by 2 to find the area of each triangle. Finally, calculate the perimeter by adding the lengths of all sides.
Step-by-step explanation:
To find the perimeter of the pattern, we need to first find the dimensions of the rectangle. We know that the area of the square is 36 cm², so the side length of the square would be √36 = 6 cm.
The area of the rectangle is 1 and a third times bigger than the square, so the area of the rectangle would be 36 × (1 + 1/3) = 36 × 4/3 = 48 cm².
The rectangle can be split into two identical triangles, so each triangle has an area of 48/2 = 24 cm².
Since the triangles have equal sides as the square, each side of the triangle would be √24 = 2√6 cm.
The perimeter of the pattern can be calculated by adding the lengths of all sides, which would be 4 × 2√6 = 8√6 cm.
Using a calculator, the approximate value of 8√6 is 21.34 cm.
Therefore, the perimeter of the pattern is approximately 21.34 cm, which is closest to option b) 30 cm.