2016 AMC 8 Problems/Problem 2
In rectangle , and . Point is the midpoint of . What is the area of ?
Solution 1
Use the triangle area formula for triangles: where is the area, is the base, and is the height. This equation gives us .
Solution 2
A triangle with the same height and base as a rectangle is half of the rectangle's area. This means that a triangle with half of the base of the rectangle and also the same height means its area is one quarter of the rectangle's area. Therefore, we get .
Solution 3(a check)
We can find the area of the entire rectangle, DCBA to be and find DCM area to be and BCA to be .
Video Solution
https://www.youtube.com/watch?v=LqnQQcUVJmA (has questions 1-5)
2016 AMC 8 (Problems • Answer Key • Resources) | ||
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