To calculate the area of quadrilateral A when you know that quadrilaterals A and B are similar, you can use the concept of similarity ratios. The ratio of corresponding sides of similar figures is equal to the square of the ratio of their corresponding lengths. In this case, you are given the lengths of sides A and B for both quadrilaterals.
Given:
Length of side A for quadrilateral A = 3 cm
Length of side B for quadrilateral A = 9 cm
Area of quadrilateral B = 63 cm²
Now, you can set up the similarity ratio for the sides of the two quadrilaterals:
Ratio of corresponding sides = (Length of side A for quadrilateral A) / (Length of side B for quadrilateral A)
Ratio of corresponding sides = 3 cm / 9 cm = 1/3
Since area is a two-dimensional measurement, the area ratio will be the square of the side ratio:
Area ratio = (1/3)² = 1/9
Now, you know the area ratio between quadrilaterals A and B is 1/9. To find the area of quadrilateral A, you can multiply the area of quadrilateral B (which is 63 cm²) by this area ratio:
Area of quadrilateral A = Area ratio * Area of quadrilateral B
Area of quadrilateral A = (1/9) * 63 cm² = 7 cm²
So, the area of quadrilateral A is 7 cm².