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Explore the Back-StoryTry this beautiful Problem on Geometry from Trapezium from (AMC 10 A, 2009).

Convex quadrilateral has and . Diagonals and intersect at , and and have equal areas. What is

,

Geometry

**quadrilateral**

Similarity

Pre College Mathematics

AMC-10A, 2009 Problem-23

Given that Convex quadrilateral has and . Diagonals and intersect at , and and have equal areas. we have to find out the length of .

Now if we can show that and are similar then we can find out ?

Can you find out?

Given that area of and area of are equal. Now area of = area of +

Area of = area of +

Therefore area of = area of [as area of and area of are equal]

Since triangles and share a base, they also have the same height and thus and with a ratio of 3: 4

Can you finish the problem?

Therefore so

- https://www.cheenta.com/surface-area-of-cube-amc-10a-2007-problem-21/
- https://www.youtube.com/watch?v=y-8Ru_qKDxk

Try this beautiful Problem on Geometry from Trapezium from (AMC 10 A, 2009).

Convex quadrilateral has and . Diagonals and intersect at , and and have equal areas. What is

,

Geometry

**quadrilateral**

Similarity

Pre College Mathematics

AMC-10A, 2009 Problem-23

Given that Convex quadrilateral has and . Diagonals and intersect at , and and have equal areas. we have to find out the length of .

Now if we can show that and are similar then we can find out ?

Can you find out?

Given that area of and area of are equal. Now area of = area of +

Area of = area of +

Therefore area of = area of [as area of and area of are equal]

Since triangles and share a base, they also have the same height and thus and with a ratio of 3: 4

Can you finish the problem?

Therefore so

- https://www.cheenta.com/surface-area-of-cube-amc-10a-2007-problem-21/
- https://www.youtube.com/watch?v=y-8Ru_qKDxk

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