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2019 AMC 8 Question 4

Zong Ellen的相片
2019 AMC 8 Question 4
Zong Ellen發表於2020年 04月 9日(Thu) 00:45

Quadrilateral ABCD is a rhombus with perimeter 52 meters.  The length of diagonal AC is 24 meters. What is the area in square meters of rhombus ABCD? 

Lensmire John的相片
Re: 2019 AMC 8 Question 4
Lensmire John發表於2020年 04月 9日(Thu) 12:14

Remember that a rhombus has $4$ sides that all have the same length. Thus since we know the perimeter we can find the length of each side.

We know that diagonal $AC$ has length $24$. What happens if we also draw diagonal $BD$ in the diagram? This divides the rhombus into 4 smaller shapes. What is nice about these shapes?