MathDB

11

Part of 2016 AMC 10

Problems(2)

Weird Area

Source: 2016 AMC 10A #11, 2016 AMC 12A #8

2/3/2016
What is the area of the shaded region of the given 8×58 \times 5 rectangle?
[asy]
size(6cm); defaultpen(fontsize(9pt)); draw((0,0)--(8,0)--(8,5)--(0,5)--cycle); filldraw((7,0)--(8,0)--(8,1)--(0,4)--(0,5)--(1,5)--cycle,gray(0.8));
label("11",(1/2,5),dir(90)); label("77",(9/2,5),dir(90));
label("11",(8,1/2),dir(0)); label("44",(8,3),dir(0));
label("11",(15/2,0),dir(270)); label("77",(7/2,0),dir(270));
label("11",(0,9/2),dir(180)); label("44",(0,2),dir(180));
[/asy]
<spanclass=′latex−bold′>(A)</span> 435<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 514<spanclass=′latex−bold′>(D)</span> 612<spanclass=′latex−bold′>(E)</span> 8<span class='latex-bold'>(A)</span>\ 4\dfrac{3}{5} \qquad <span class='latex-bold'>(B)</span>\ 5\qquad <span class='latex-bold'>(C)</span>\ 5\dfrac{1}{4} \qquad <span class='latex-bold'>(D)</span>\ 6\dfrac{1}{2} \qquad <span class='latex-bold'>(E)</span>\ 8
AMCAMC 10AMC 10 AgeometryAMC 12mathematicsTriangles
Carl The Garden Fencer

Source: Problem #11 2016 AMC 10B and #9 AMC 12

2/21/2016
Carl decided to fence in his rectangular garden. He bought 2020 fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly 44 yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden?
<spanclass=′latex−bold′>(A)</span> 256<spanclass=′latex−bold′>(B)</span> 336<spanclass=′latex−bold′>(C)</span> 384<spanclass=′latex−bold′>(D)</span> 448<spanclass=′latex−bold′>(E)</span> 512<span class='latex-bold'>(A)</span>\ 256\qquad<span class='latex-bold'>(B)</span>\ 336\qquad<span class='latex-bold'>(C)</span>\ 384\qquad<span class='latex-bold'>(D)</span>\ 448\qquad<span class='latex-bold'>(E)</span>\ 512
AMCAMC 102016 AMC 10BAMC 10 B