MathDB

2

Part of 2021 AMC 10 Fall

Problems(2)

Menkara and Index Cards

Source: 2021 AMC 10A/12A (Fall) #2

11/11/2021
Menkara has a 4×64 \times 6 index card. If she shortens the length of one side of this card by 11 inch, the card would have area 1818 square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by 11 inch?
<spanclass=′latex−bold′>(A)</span>16<spanclass=′latex−bold′>(B)</span>17<spanclass=′latex−bold′>(C)</span>18<spanclass=′latex−bold′>(D)</span>19<spanclass=′latex−bold′>(E)</span>20<span class='latex-bold'>(A) </span>16\qquad<span class='latex-bold'>(B) </span>17\qquad<span class='latex-bold'>(C) </span>18\qquad<span class='latex-bold'>(D) </span>19\qquad<span class='latex-bold'>(E) </span>20
AMCAMC 10AMC 10 Aamc12a
Complementary Counting

Source: 2021 Fall AMC 10/12 B #2

11/17/2021
What is the area of the shaded figure shown below?
[asy] size(200); defaultpen(linewidth(0.4)+fontsize(12)); pen s = linewidth(0.8)+fontsize(8);
pair O,X,Y; O = origin; X = (6,0); Y = (0,5); fill((1,0)--(3,5)--(5,0)--(3,2)--cycle, palegray+opacity(0.2)); for (int i=1; i<7; ++i) { draw((i,0)--(i,5), gray+dashed); label(""+string(i)+"{"+string(i)+"}", (i,0), 2*S); if (i<6) { draw((0,i)--(6,i), gray+dashed); label(""+string(i)+"{"+string(i)+"}", (0,i), 2*W); } } label("00", O, 2*SW); draw(O--X+(0.15,0), EndArrow); draw(O--Y+(0,0.15), EndArrow); draw((1,0)--(3,5)--(5,0)--(3,2)--(1,0), black+1.5); [/asy]
complementary countingAMC 12 BAMC 10 BAMCAMC 10AMC 12