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# 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

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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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

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

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