Final answer:
To express the relation as a variation statement, we use the equation A = k × b × h. From the given values, we can solve for k and find that k = 0.5. Using the variation statement, we can then find the value of A when given new values for b and h.
Step-by-step explanation:
To express the relation as a variation statement, we need to determine how the area (A) varies with the base (b) and height (h) of a shape. In the first case, when the area is 15cm², and the base is 5cm and height is 6cm, we can write the variation statement as: A is directly proportional to b and h. Therefore, we have A = k × b × h. To find the value of k, we substitute the given values into the equation: 15 = k × 5 × 6. Solving for k, we find k = 0.5.
In the second case, we are given that A = 65cm² when b = 10cm and h = 13cm. We are asked to find A when b = 8cm and h = 11cm. Using the variation statement A = k × b × h, we substitute the given values into the equation: A = 0.5 × 8 × 11. Solving for A, we find A = 44cm².