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 ?
2D - Geometry
Isosceles Triangle
Area of Triangle
But try the problem first...
Answer: 24
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).
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
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 ?
2D - Geometry
Isosceles Triangle
Area of Triangle
But try the problem first...
Answer: 24
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).
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
