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1260 cm^2

Step-by-step explanation:

To find the area of the rectangle we need its base and its height and calculate the product A = (base)(height).

Here the height of the triangle is found using the Pythagorean Theorem:

37^2 = |AB|^2 + 12^2, or |AB|^2 = 1369 - 144, or 1225.

Taking the square root of both sides, we get |AB| = √1225  =  35 cm = height of rectangle.

Since BC:CD = 1:2, and since |BC| = 12 cm, |BD| is 12 cm + 24 cm = 36 cm.

Thus the length of the rectangle is 36 cm.

The area of the rectangle ABDE is (36 cm)(35 cm) = 1260 cm^2

d

step-by-step explanation:

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step-by-step explanation: