1956 AHSME Problems/Problem 35

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Solution

First, we create a circle and its $2$ radii. Both of these have length $16$. When we join them, we get our first chord. Let's call this $AB$. Now, we can create two more chords of our own choice, as long as both of them start from points $A$ and $B$ respectively and our final figure looks like a rhombus. Let's call these newly created points $C$ and $D$. Thus, now we have our rhombus $ABCD$. Since we known the formula for a rhombus's area is $A = \frac{pq}{2}$, we can now successfully substitute the $p$ and the $q$ both with $16 feet$ (since, in our case, we had a circle, both our $p$ and $q$ are going to be the same). After substituting, we get: $\frac{16*16}{2}$; upon using arithmetic, we yield our answer to be $128 feet^2$.

-Solution by DRAGONWARRIOR123

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