2005 CEMC Gauss (Grade 7) Problems/Problem 15
Contents
Problem
In the diagram, the area of rectangle is . If , what is the area of quadrilateral ?
Solution 1
Since the area of rectangle is , let us assume that and . Since , then so . Therefore, triangle has base of length and height of length 2, so its area is . So the area of quadrilateral is equal to the area of rectangle (which is ) minus the area of triangle (which is ), or . Therefore, the answer is .
Solution 2
Draw a line through parallel to across the rectangle parallel so that it cuts at point . Since is halfway between and , then is halfway between and . Therefore, is a rectangle which has an area equal to half the area of rectangle , or . Similarly, is a rectangle of area , and is cut in half by , so triangle has area . Therefore, the area of is equal to the sum of the area of the rectangle and the area of triangle , or . The correct answer is .
See Also
2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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CEMC Gauss (Grade 7) |