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
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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