Find the area. abcd∼efghabcd∼efgh the area of rectangle abcd is 72 inches2 and a diagonal is 12 inches. the diagonal of rectangle efgh is 22 inches. find the area of rectangle efgh. round to the nearest inch2 if necessary.

Since the two figures are similar, it can be deduced that the corresponding sides, including the diagonals, will have a common ratio. This ratio is,
                    d₁ / d₂ = 12 inches / 22 inches

The ratio of their areas should be the square of this ratio.

If we let x be the area of the larger rectangle, we have the equation,
 
                      A₁ / A₂ = (d₁/d₂)²  = (72 inches² / x inches²)

Substituting the known values,
 
                        (12 /22)² = (72 inches² / x inches²)

The value of x is equal to 242 inches². Thus, the area of the larger rectangle is 242 inches².