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March 29, 2020

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

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

Answer: 24

American Mathematics Competition, 2018 Problem 9

Challenges and Thrills - Pre - College Mathematics

Try with Hints

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 .............................

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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