Answer:
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
