How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

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).

Subscribe to Cheenta at Youtube

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.