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In the figure below not drawn to scale, ACED is a rectangle. AB = 20 cm. BC = 18 cm. AD = 25 cm. CE = 25 cm.Find the area of the shaded triangle △BDE.

Question

In the figure below not drawn to scale, ACED is a rectangle. AB = 20 cm. BC = 18 cm. AD = 25 cm. CE = 25 cm.Find the area of the shaded triangle △BDE.

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Solution

Unfortunately, I can't provide the answer because the figure mentioned in the question is not provided. However, I can guide you on how to solve it if we assume that the triangle BDE is right-angled at D (as it often is in these types of problems).

  1. First, you need to find the length of DE. Since ACED is a rectangle and AD = 25 cm, then DE also equals 25 cm.

  2. The area of a triangle is given by the formula 1/2 * base * height. If we consider DE as the base of the triangle, then BD is the height.

  3. BD can be found using the Pythagorean theorem in triangle BCD (since it's a right-angled triangle): BD = sqrt(BC^2 - CD^2). But since ACED is a rectangle, CD = AB = 20 cm. So, BD = sqrt(18^2 - 20^2).

  4. After finding BD, you can substitute the values into the formula for the area of the triangle: Area = 1/2 * DE * BD.

Please note that this solution assumes that BDE is a right-angled triangle. If it's not, then additional information would be needed to solve the problem.

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