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

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

2D - Geometry

Isosceles Triangle

Area of Triangle

But try the problem first...

Answer: 24

Source

Suggested Reading

American Mathematics Competition, 2018 Problem 9

Challenges and Thrills - Pre - College Mathematics

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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