Problem:
Consider these two geoboard quadrilaterals. Which of the following statements is true?
Answer Choices:
A. The area of quadrilateral is more than the area of quadrilateral .
B. The area of quadrilateral is less than the area of quadrilateral .
C. The quadrilaterals have the same area and the same perimeter.
D. The quadrilaterals have the same area, but the perimeter of is more than the perimeter of .
E. The quadrilaterals have the same area, but the perimeter of is less than the perimeter of .
Solution:
Divide each quadrilateral as shown. The resulting triangles each have base , altitude , and area , so the quadrilaterals each have area .
Three sides of quadrilateral match those of quadrilateral as indicated by matching marks. The fourth side of quadrilateral is less than the fourth side of quadrilateral , hence its perimeter is less, and choice is correct.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions