Difference between revisions of "1954 AHSME Problems/Problem 5"

 
Line 7: Line 7:
 
== Solution ==
 
== Solution ==
 
Using the formula for the area of a hexagon given the circumradius: <math>\frac{3\sqrt{3}}{2\pi}=\frac{A}{10^2\pi}\implies 100\cdot3\sqrt{3}\pi=2A\pi\implies 50\cdot3\sqrt{3}=A\implies 150\sqrt{3}\ \boxed{(\textbf{A})}</math>
 
Using the formula for the area of a hexagon given the circumradius: <math>\frac{3\sqrt{3}}{2\pi}=\frac{A}{10^2\pi}\implies 100\cdot3\sqrt{3}\pi=2A\pi\implies 50\cdot3\sqrt{3}=A\implies 150\sqrt{3}\ \boxed{(\textbf{A})}</math>
 +
 +
==See Also==
 +
 +
{{AHSME 50p box|year=1954|num-b=4|num-a=6}}
 +
 +
{{MAA Notice}}

Latest revision as of 19:36, 17 February 2020

Problem 5

A regular hexagon is inscribed in a circle of radius $10$ inches. Its area is:

$\textbf{(A)}\ 150\sqrt{3} \text{ sq. in.} \qquad \textbf{(B)}\ \text{150 sq. in.} \qquad \textbf{(C)}\ 25\sqrt{3}\text{ sq. in.}\qquad\textbf{(D)}\ \text{600 sq. in.}\qquad\textbf{(E)}\ 300\sqrt{3}\text{ sq. in.}$

Solution

Using the formula for the area of a hexagon given the circumradius: $\frac{3\sqrt{3}}{2\pi}=\frac{A}{10^2\pi}\implies 100\cdot3\sqrt{3}\pi=2A\pi\implies 50\cdot3\sqrt{3}=A\implies 150\sqrt{3}\ \boxed{(\textbf{A})}$

See Also

1954 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions


The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png