MathDB
Batman Returns! (kind of)

Source: 2016 AMC 8 #22

November 23, 2016
AMC 8geometryrectangle2016 AMC 8

Problem Statement

Rectangle DEFADEFA below is a 3×43 \times 4 rectangle with DC=CB=BADC=CB=BA. The area of the "bat wings" is [asy] size(180); defaultpen(fontsize(11pt)); draw((0,0)--(3,0)--(3,4)--(0,4)--(0,0)--(2,4)--(3,0)); draw((3,0)--(1,4)--(0,0)); fill((0,0)--(1,4)--(1.5,3)--cycle, black); fill((3,0)--(2,4)--(1.5,3)--cycle, black); label("DD",(0,4),NW); label("CC",(1,4),N); label("BB",(2,4),N); label("AA",(3,4),NE); label("EE",(0,0),SW); label("FF",(3,0),SE);[/asy] <spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>212<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>312<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>2 \frac{1}{2}\qquad<span class='latex-bold'>(C) </span>3\qquad<span class='latex-bold'>(D) </span>3 \frac{1}{2}\qquad <span class='latex-bold'>(E) </span>5