¶ 2019 AMC8 Problem 4
Problem:
Quadrilateral is a rhombus with a perimeter of meters. The length of diagonal is meters. What is the area in square meters of rhombus
Answer Choices:
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Solution:
Let be the midpoint of . Then . Because the diagonals of a rhombus are perpendicular and bisect each other, is perpendicular to . Because all four sides of a rhombus have the same length, . By the Pythagorean Theorem, = 5. The area of is square meters. Thus the area of rhombus is square meters.
As above, , and So As above, . The area of a rhombus is one-half the product of the lengths of the diagonals. The area of is therefore square meters.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions