Difference between revisions of "2022 AMC 8 Problems/Problem 1"
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| − | Note that the given symbol can be split into <math>5</math> diamonds. Each of the diamonds | + | Note that the given symbol can be split into <math>5</math> diamonds. Each of the diamonds contain <math>4</math> triangles, so each of the diamonds has an area of <math>0.5 \cdot 4 = 2</math>. Hence, our answer is <math>2 \cdot 5 = \boxed{\textbf{(A) }10}</math>. |
<i>pog</i> | <i>pog</i> | ||
Revision as of 09:24, 28 January 2022
Problem
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
![[asy] usepackage("mathptmx"); defaultpen(linewidth(0.5)); size(5cm); defaultpen(fontsize(14pt)); label("$\textbf{Math}$", (2.1,3.7)--(3.9,3.7)); label("$\textbf{Team}$", (2.1,3)--(3.9,3)); filldraw((1,2)--(2,1)--(3,2)--(4,1)--(5,2)--(4,3)--(5,4)--(4,5)--(3,4)--(2,5)--(1,4)--(2,3)--(1,2)--cycle, mediumgray*0.5 + lightgray*0.5); draw((0,0)--(6,0), gray); draw((0,1)--(6,1), gray); draw((0,2)--(6,2), gray); draw((0,3)--(6,3), gray); draw((0,4)--(6,4), gray); draw((0,5)--(6,5), gray); draw((0,6)--(6,6), gray); draw((0,0)--(0,6), gray); draw((1,0)--(1,6), gray); draw((2,0)--(2,6), gray); draw((3,0)--(3,6), gray); draw((4,0)--(4,6), gray); draw((5,0)--(5,6), gray); draw((6,0)--(6,6), gray); [/asy]](http://latex.artofproblemsolving.com/3/6/0/3601cfc2de44b936af89add318708b5a995aff67.png)
Solution
Note that the given symbol can be split into 
diamonds. Each of the diamonds contain 
triangles, so each of the diamonds has an area of 
. Hence, our answer is 
.
pog
See also
| 2022 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
