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AMC 12 USA Math Olympiad

Area of Trapezoid | AMC 10A, 2018 | Problem 9

Try this beautiful problem from AMC 10A, 2018 based on area of trapezoid. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC 10A, 2018 based on area of trapezoid.

Area of Trapezoid | AMC 10A


All of the triangles in the diagram below are similar to isosceles triangle ABC , in which AB = AC . Each of the 7 smallest triangles has area 1 and \(\triangle {ABC}\) has area 40.  What is the area of trapezoid DBCE ?

  • 24
  • 25
  • 26
  • 20

Key Concepts


2D – Geometry

Isosceles Triangle

Area of Triangle

Check the Answer


But try the problem first…

Answer: 24

Source
Suggested Reading

American Mathematics Competition, 2018 Problem 9

Challenges and Thrills – Pre – College Mathematics

Try with Hints


First hint

We can try this problem using this hint :

Let the base length of the small triangle be  x :

Then, there is a triangle ADE encompassing the 7 small triangles and sharing the top angle with a base length of 4x.

Try the rest of the sum ………………………..

Second Hint

Continuing from the last hint:

Because the area is proportional to the square of the side, let the base BC be \(\sqrt {40}x\). Then triangle ADE  has an area of 16. So the area is 40 – 16 = 24(Answer).

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