2025년 6월 20일 금요일

국제 올림피아드 영재 교육… 삼성·한화서 지원한다…기업 첫 후원

삼성·한화 등 민간 기업들이 국제 올림피아드에 출전하는 한국 대표단 비용을 후원한다. 기업이 올림피아드 대표단을 공식 후원하는 첫 사례다. 최근 10년간 국제 올림피아드 대표단을 지원하는 정부 예산이 계속 줄어들고, 과학·수학 영재 양성의 차질을 우려하는 목소리가 커지자, 국내 주요 기업들이 지원하겠다고 나선 것이다. 과학·산업계에 따르면, 삼성전자와 한화생명은 26일 한국과학창의재단과 ‘국제 수학·물리 올림피아드 한국대표단 양성을 위한 후원 협약 체결’을 한다. 삼성전자의 디바이스솔루션(DS) 부문은 국제 물리 올림피아드 대표단을, 디바이스경험(DX) 부문은 국제 수학 올림피아드 대표단을 후원할 예정이다. 한화생명은 국제 정보 올림피아드에 출전하는 대표단을 후원하기로 한 것으로 알려졌다. 삼성전자와 한화생명은 앞으로 국제 올림피아드 한국 대표단이 출전 전에 진행하는 각종 합숙 교육과 실험 교육 및 기자재, 국제 대회 출전 비용 전반, 우수 학생에게 주는 장학금까지 패키지로 연간 억대 비용을 후원한다. 이 회사들이 올림피아드 한국 대표단을 돕기로 한 주요 배경에 과학·수학 영재 교육의 위기가 있다. 국제 올림피아드 대회를 향한 국민적 관심이 차츰 식으면서 지원 예산도 줄고 성적이 내려앉은 것이다. 한국은 10여 년 전만 해도 수학, 물리, 정보, 화학, 생물, 등 주요 과목에서 가장 많은 학생이 금메달을 따내며 종합 1위를 휩쓸다시피 한 올림피아드 강국이었다. 2014년 교육부가 ‘국제 올림피아드 수상’ 실적을 대입에 반영하지 못하게 규제한 것을 계기로 올림피아드 지원자가 줄기 시작했다. 예컨대 2023년 국제과학올림피아드 지원자 수는 2508명으로 2014년(3982명)보다 37% 줄었다. 성적도 예전 같지 않다. 작년 한국의 국제 올림피아드 화학 부문 종합 성적은 20위에 그쳤다. 정부 예산은 2010년 약 20억원에서 2024년 약 17억원으로 15%가량 감소했다. 윤진희 한국물리학회장은 “중국과 미국은 국제 올림피아드에 출전하는 대표 선수단 교육에 매년 상당한 예산을 쏟고 있고 장학금 지원도 파격적으로 해주고 있다”면서 “반면 우리는 대표 선수단의 외국 대회 참가 비용도 넉넉하지 않아 기업들의 후원 확대가 절실하다”고 했다. 조선일보
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2025년 4월 19일 토요일

경북대학교 과학영재교육원 신입생 선발(현재 초6· 중1학년대상) 모집요강

모집 인원, 선발 일정 등 자세한 내용은 모집요강(첨부파일)을 확인 바랍니다. 2025학년도 경북대학교 과학영재교육원 신입생 선발은 GED시스템(영재교육종합데이터베이스)에서 진행됩니다. GED 시스템: https://ged.kedi.re.kr (주의: 꼭 크롬브라우저를 이용하세요.) ♦ 2025학년도 경북대학교 과학영재교육원 신입생 선발(현재 초6· 중1학년대상) 모집요강 보러가기(클릭!!) ♦ (아래 첨부파일에서도 확인가능) 2025학년도 경북대학교 과학영재교육원 신입생 선발 (중등과정-현재 초 6학년·중1학년 대상) 모집 요강 공고 - 공고일: 2024. 9. 6.(금) - 모집 인원, 선발 일정 등 자세한 내용은 모집요강(첨부파일)을 확인 바랍니다. 2025학년도 경북대학교 과학영재교육원 신입생 선발은 GED시스템(영재교육종합데이터베이스)에서 진행됩니다. GED 시스템: https://ged.kedi.re.kr (주의: 꼭 크롬브라우저를 이용하세요.) ♦ 2025학년도 경북대학교 과학영재교육원 신입생 선발(현재 초6· 중1학년대상) 모집요강 보러가기(클릭!!) ♦ (아래 첨부파일에서도 확인가능)
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2025년 3월 22일 토요일

중국이 공장에서 천재를 찍어내고 있습니다 (딥시크 )


중국이 공장에서 천재를 찍어내고 있습니다 (딥시크 )
Deep Seek
영재 말고 중국의 천재교육
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2025년 3월 8일 토요일

2025 AMC 8 Problems

 

Problem 1

The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4×4 grid is covered by the star?


[asy] path x = (0,1)--(1,2)--(2,2)--(1,1)--cycle; path y = reflect((0,0),(4,4)) * x; fill(x, gray(0.6)); fill(rotate(90, (2,2)) * x, gray(0.6)); fill(rotate(180, (2,2)) * x, gray(0.6)); fill(rotate(270, (2,2)) * x, gray(0.6)); fill(y, gray(0.8)); fill(rotate(90, (2,2)) * y, gray(0.8)); fill(rotate(180, (2,2)) * y, gray(0.8)); fill(rotate(270, (2,2)) * y, gray(0.8)); draw((1,1)--(3,3)); draw((3,1)--(1,3)); add(grid(4,4)); path w = (1,0)--(2,1)--(3,0); draw(w); draw(rotate(90, (2,2)) * w); draw(rotate(180, (2,2)) * w); draw(rotate(270, (2,2)) * w); [/asy]

$\textbf{(A)}\ 40 \qquad \textbf{(B)}\ 50 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 80$

Solution

Problem 2

The table below shows the Ancient Egyptian hieroglyphs that were used to represent different numbers. Mathh.PNG

For example, the number $32$ was represented by the hieroglyphs $\cap \cap \cap ||$. What number is represented by the following combination of hieroglyphs?

Amc8 2025 prob 2 pic.PNG

$\textbf{(A)}\ 1,423 \qquad \textbf{(B)}\ 10,423 \qquad \textbf{(C)}\ 14,023 \qquad \textbf{(D)}\ 14,203 \qquad \textbf{(E)}\ 14,230$

Solution

Problem 3

Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game. When Annika and $3$ of her friends play Buffalo Shuffle-o, each player is dealt $15$ cards. Suppose $2$ more friends join the next game. How many cards will be dealt to each player?

$\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 11 \qquad \textbf{(E)}\ 12$

Solution

Problem 4

Lucius is counting backward by $7$s. His first three numbers are $100$, $93$, and $86$. What is his $10$th number?

$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 37 \qquad \textbf{(C)}\ 42 \qquad \textbf{(D)}\ 44 \qquad \textbf{(E)}\ 47$

Solution

Problem 5

Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labled $F$) and drives to location $A$, then $B$, then $C$, before returning to $F$. What is the shortest distance, in blocks, she can drive to complete the route?

[asy] unitsize(20); add(grid(8,6)); path w = circle((0,0),0.4); fill(w, white); draw(w); label("$B$",(0,0)); fill(shift((2,4)) * w, white); draw(shift((2,4)) * w); label("$C$",(2,4)); fill(shift((7,3)) * w, white); draw(shift((7,3)) * w); label("$A$",(7,3)); fill(shift((6,5)) * w, white); draw(shift((6,5)) * w); label("$F$",(6,5)); draw((6,-0.2)--(7,-0.2), EndArrow(3)); draw((7,-0.2)--(6,-0.2), EndArrow(3)); draw(shift(6.5, -0.48) * scale(0.03) * texpath("1 block")); draw((8.2,1)--(8.2,2), EndArrow(3)); draw((8.2,2)--(8.2,1), EndArrow(3)); draw(shift(8.88, 1.5) * scale(0.03) * texpath("1 block")); [/asy]

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 22 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 26\qquad \textbf{(E)}\ 28$

Solution

Problem 6

Sekou writes the numbers $15, 16, 17, 18, 19.$ After he erases one of his numbers, the sum of the remaining four numbers is a multiple of $4.$ Which number did he erase?

$\textbf{(A)}\ 15\qquad \textbf{(B)}\ 16\qquad \textbf{(C)}\ 17\qquad \textbf{(D)}\ 18\qquad \textbf{(E)}\ 19$

Solution

Problem 7

On the most recent exam on Prof. Xochi's class,

$5$ students earned a score of at least $95\%$,
$13$ students earned a score of at least $90\%$, 
$27$ students earned a score of at least $85\%$,
$50$ students earned a score of at least $80\%$.

How many students earned a score of at least 80% and less than 90%?

$\textbf{(A)}\ 8\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 22\qquad \textbf{(D)}\ 37\qquad \textbf{(E)}\ 45$

Solution

Problem 8

Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?

Amc8 2025 prob8.PNG

$\textbf{(A)}~3\sqrt{3}\qquad\textbf{(B)}~6\qquad\textbf{(C)}~9\qquad\textbf{(D)}~6\sqrt{3}\qquad\textbf{(E)}~9\sqrt{3}$

Solution

Problem 9

Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of numbers. What is the average of the resulting 6 numbers?

[asy] /* AMC8 P9 2025, by NUMANA: BUI VAN HIEU buivanhieu@husc.edu.vn, https://husc.edu.vn */ unitsize(1cm); draw(circle((0,0),2)); for(int i = 1; i <= 12; ++i) { draw(1.9*dir(90-i*30)-- 2*dir(90-i*30));//,linewidth(1pt) label("$"+string(i)+"$",2.3*dir(90-i*30)); } draw(2*dir(-150)--2*dir(30),dashed); [/asy]

$\textbf{(A)}\ 5\qquad \textbf{(B)}\ 6.5\qquad \textbf{(C)}\ 8\qquad \textbf{(D)}\ 9.5 \qquad \textbf{(E)}\ 12$

Solution

Problem 10

In the figure below, $ABCD$ is a rectangle with sides of length $AB = 5$ inches and $AD$ = 3 inches. Rectangle $ABCD$ is rotated $90^\circ$ clockwise around the midpoint of side $DC$ to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?

Amc8 2025 prob10.PNG


$\textbf{(A)}\ 21 \qquad \textbf{(B)}\ 22.25 \qquad \textbf{(C)}\ 23 \qquad \textbf{(D)}\ 23.75 \qquad \textbf{(E)}\ 25$

Solution

Problem 11

A $\textit{tetromino}$ consists of four squares connected along their edges. There are five possible tetromino shapes, $I$, $O$, $L$, $T$, and $S$, shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a $3\times4$ rectangle. At least one of the tiles is an $S$ tile. What are the other two tiles?

[asy] unitsize(12); add(grid(1,4)); label("I", (0.5,-1)); add(shift((5,0)) * grid(2,2)); label("O", (6,-1)); add(shift((11,0)) * grid(1,3)); add(shift((11,0)) * grid(2,1)); label("L", (12,-1)); add(shift((18,0)) * grid(1,1)); add(shift((17,1)) * grid(3,1)); label("T", (18.5,-1)); add(shift((25,1)) * grid(2,1)); add(shift((24,0)) * grid(2,1)); label("S", (25.5,-1)); add(shift((12,-6)) * grid(4,3)); [/asy]

$\textbf{(A)}I$ and $L\qquad \textbf{(B)} I$ and $T\qquad \textbf{(C)} L$ and $L\qquad \textbf{(D)}L$ and $S\qquad \textbf{(E)}O$ and $T$

Solution

Problem 12

The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?

[asy] import graph; size(100); pen gridPen = black; void drawSquare(pair p) { draw(box(p, p + (1,1)), gridPen); } int[][] grid = { {0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 0}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {0, 1, 1, 1, 1, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0} }; int rows = grid.length; int cols = grid[0].length; for (int i = 0; i < rows; ++i) { for (int j = 0; j < cols; ++j) { if (grid[i][j] == 1) { drawSquare((j, rows - i - 1)); } } } [/asy]

$\textbf{(A)}\ 3\pi\qquad \textbf{(B)}\ 4\pi\qquad \textbf{(C)}\ 5\pi\qquad \textbf{(D)}\ 6\pi\qquad \textbf{(E)}\ 8\pi$

Solution

Problem 13

Each of the even numbers $2, 4, 6, \ldots, 50$ is divided by $7$. The remainders are recorded. Which histogram displays the number of times each remainder occurs?[asy] /*By Reda_mandymath*/ unitsize(15); void histogram(pair p, string _str, int[] n) { /* p is shift transformation, _str is choice string, n[] is the array of number of remainders, _pen is the pen style of block, a is the width of block, b is the width of gap _scale is the font scale of labels*/ pen _pen; real a = 0.8; real b = 0.3; real _scale = 0.8; draw(shift(p) * ((0, 0) -- (9, 0) -- (9, 5) -- (0, 5) -- cycle)); label(scale(_scale) * rotate(90) * "Count", (-0.4, 2.5)+p); label(scale(_scale) * "Remainder", (4.5, -1)+p); for (int i = 0; i <= 6; ++i) { if (n[i] == 3) { _pen = mediumgray; } else { _pen = heavygray; } fill(shift(p) * ((a*(i+1) + b*i, 0) -- (a*(i+1) + b*i, n[i]) -- (a*(i+2) + b*i, n[i]) -- (a*(i+2) + b*i, 0) -- cycle), _pen); label(scale(_scale) * string(i), shift(p) * (a*(i+1.5) + b*i, 0), S); label(scale(_scale) * string(n[i]), shift(p) * (a*(i+1.5) + b*i, n[i]), N); } label(_str, shift(p) * (-0.4, 6)); } histogram((0, 0), "$\textbf{(A)}$", new int[] {3, 4, 4, 3, 4, 3, 4}); histogram((12, 0), "$\textbf{(B)}$", new int[] {3, 4, 4, 4, 3, 3, 4}); histogram((24, 0), "$\textbf{(C)}$", new int[] {3, 4, 4, 4, 4, 3, 3}); histogram((0, -8), "$\textbf{(D)}$", new int[] {4, 3, 4, 3, 4, 3, 4}); histogram((12, -8), "$\textbf{(E)}$", new int[] {4, 4, 3, 4, 3, 4, 3}); [/asy]Solution

Problem 14

A number $N$ is inserted into the list $2, 6, 7, 7, 28$. The mean is now twice as great as the median. What is $N$?

$\textbf{(A)}\ 7\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 20\qquad \textbf{(D)}\ 28\qquad \textbf{(E)}\ 34$

Solution

Problem 15

Kei draws a $6$-by-$6$ grid. He colors $13$ of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let $m$ and $M$ equal the least and greatest possible number of gold-on-gold pairs, respectively. What is the value of $m+M$?

[asy] import graph; size(100); pen gridPen = black; void drawSquare(pair p) { draw(box(p, p + (1,1)), gridPen); } int[][] grid = { {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, }; int rows = grid.length; int cols = grid[0].length; for (int i = 0; i < rows; ++i) { for (int j = 0; j < cols; ++j) { if (grid[i][j] == 1) { drawSquare((j, rows - i - 1)); } } } [/asy]

$\textbf{(A)}\ 12\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 16\qquad \textbf{(D)}\ 18 \qquad \textbf{(E)}\ 20$

Solution

Problem 16

Five distinct integers from $1$ to $10$ are chosen, and five distinct integers from $11$ to $20$ are chosen. No two numbers differ by exactly $10$. What is the sum of the ten chosen numbers?

$\textbf{(A)}\ 95\qquad \textbf{(B)}\ 100\qquad \textbf{(C)}\ 105\qquad \textbf{(D)}\ 110\qquad \textbf{(E)}\ 115$

Solution

Problem 17

In the land of Markovia, there are three cities: $A$, $B$, and $C$. There are $100$ people who live in $A$, $120$ who live in $B$, and $160$ who live in $C$. Everyone works in one of the three cities, and a person may work in the same city where they live. In the figure below, an arrow pointing from one city to another is labeled with the fraction of people living in the first city who work in the second city. (For example, $\frac{1}{4}$ of the people who live in $A$ work in $B$.) How many people work in $A$?

[asy] /* AMC8 P17 2025, by NUMANA: BUI VAN HIEU, buivanhieu@husc.edu.vn, https://husc.edu.vn, https://husc.edu.vn */ import graph; unitsize(2cm); real r=0.15; pair A, B, C;B = (0,0);C = (2,0);A = (1,sqrt(3)); // Drawing the nodes draw(circle(A,r)); label("$A$", A); draw(circle(B,r)); label("$B$", B); draw(circle(C,r)); label("$C$", C); guide AB=A+r*dir(-135)..{down}B+r*dir(90), BA=B+r*dir(60)..{up}A+r*dir(-105), BC=B+r*dir(0)..(1,-0.2)..C+r*dir(180), CB=C+r*dir(150)..(1,0.3)..B+r*dir(30), CA=C+r*dir(90){up}..A+r*dir(-45), AC=A+r*dir(-75){down}..C+r*dir(120); draw(AB,L=Label("$1/4$", MidPoint, W),Arrow(HookHead));draw(BA,L=Label("$1/3$", MidPoint, W),Arrow(HookHead));draw(BC,L=Label("$1/6$", MidPoint, S),Arrow(HookHead));draw(CB,L=Label("$1/10$", MidPoint, S),Arrow(HookHead)); draw(CA,L=Label("$1/8$", MidPoint, E),Arrow(HookHead));draw(AC,L=Label("$1/5$", MidPoint, E),Arrow(HookHead)); [/asy]

$\textbf{(A)}\ 55\qquad \textbf{(B)}\ 60\qquad \textbf{(C)}\ 85\qquad \textbf{(D)}\ 115\qquad \textbf{(E)}\ 160$

Solution

Problem 18

The circle shown below on the left has a radius of 1 unit. The region between the circle and the inscribed square is shaded. In the circle shown on the right, one quarter of the region between the circle and the inscribed square is shaded. The shaded regions in the two circles have the same area. What is the radius $R$, in units, of the circle on the right?

[asy] unitsize(40); real a = 0.707; fill(circle((a,a), 1), grey); fill((0,0)--(0,1.414)--(1.414,1.414)--(1.414,0)--cycle, white); draw((0,0)--(0,1.414)--(1.414,1.414)--(1.414,0)--cycle); draw(circle((a,a), 1)); draw((0.707,0.707)--(1.414,1.414)); dot((0.707,0.707)); label("$1$", (1,1), SE); fill(circle((4+a, a), 2*a), grey); fill(shift((4+a,a)) * ((-2,-2)--(1,-2)--(1,2)--(-2,2)--cycle), white); draw(shift((4+a,a)) * ((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle)); draw(circle((4+a, a), 2*a)); draw((4+a,a)--(5+a,1+a)); dot((4+a,a)); label("$R$", (a+4.5,a+0.5), SE); [/asy]

$\textbf{(A)}\ \sqrt2\qquad \textbf{(B)}\ 2\qquad \textbf{(C)}\ 2\sqrt2\qquad \textbf{(D)}\ 4\qquad \textbf{(E)}\ 4\sqrt2$

Solution

Problem 19

Two towns, $A$ and $B$, are connected by a straight road, $15$ miles long. Traveling from town $A$ to town $B$, the speed limit changes every $5$ miles: from $25$ to $40$ to $20$ miles per hour (mph). Two cars, one at town $A$ and one at town $B$, start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town $A$, in miles, will the two cars meet?

$\textbf{(A)}\ 7.75\qquad \textbf{(B)}\ 8\qquad \textbf{(C)}\ 8.25\qquad \textbf{(D)}\ 8.5\qquad \textbf{(E)}\ 8.75$

Solution

Problem 20

Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?

$\textbf{(A)}\ \frac{4}{7}\qquad \textbf{(B)}\ \frac{3}{5}\qquad \textbf{(C)}\ \frac{2}{3}\qquad \textbf{(D)}\ \frac{3}{4}\qquad \textbf{(E)}\ \frac{7}{8}$

Solution

Problem 21

The Konigsberg School has assigned grades 1 through 7 to pods $A$ through $G$, one grade per pod. Some of the pods are connected by walkways, as shown in the figure below. The school noticed that each pair of connected pods has been assigned grades differing by 2 or more grade levels. (For example, grades 1 and 2 will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods $C, E$, and $F$?

2025 AMC 8 problem 21.png

$\textbf{(A)}~12\qquad\textbf{(B)}~13\qquad\textbf{(C)}~14\qquad\textbf{(D)}~15\qquad\textbf{(E)}~16$

Solution

Problem 22

A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of empty hooks before the first coat, after the last coat, and between every coat and the next one. Suppose there is at least 1 coat and at least 1 empty hook. How many different numbers of coats can satisfy Paulina's pattern?

$\textbf{(A)}\ 2\qquad \textbf{(B)}\ 4\qquad \textbf{(C)}\ 5\qquad \textbf{(D)}\ 7\qquad \textbf{(E)}\ 9$

Solution

Problem 23

How many four-digit numbers have all three of the following properties?

(I) The tens and ones digit are both 9.

(II) The number is 1 less than a perfect square.

(III) The number is the product of exactly two prime numbers.

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution

Problem 24

In trapezoid $ABCD$, angles $B$ and $C$ measure $60^\circ$ and $AB = DC$. The side lengths are all positive integers, and the perimeter of $ABCD$ is $30$ units. How many non-congruent trapezoids satisfy all of these conditions?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution

Problem 25

Makayla finds all the possible ways to draw a path in a $5 \times 5$ diamond-shaped grid. Each path starts at the bottom of the grid and ends at the top, always moving one unit northeast or northwest. She computes the area of the region between each path and the right side of the grid. Two examples are shown in the figures below. What is the sum of the areas determined by all possible paths?

[asy] unitsize(9); real a = 0.7071; path w = (0,0)--(2a, 2a)--(-a,5a)--(a,7a)--(-a,9a)--(0,10a); fill(w--(5a,5a)--cycle, gray(0.8)); draw(w, linewidth(1.5)); path x = (10,0)--(10-a,a)--(10+2a,4a)--(10-2a,8a)--(10,10a); fill(x--(10+5a,5a)--cycle, gray(0.8)); draw(x, linewidth(1.5)); add(rotate(45, (0,0)) * grid(5,5)); add(rotate(45, (10,0)) * (shift((10,0)) * grid(5,5))); dot((0,0)); dot((0,7.07106)); dot((10,0)); dot((10,7.07106)); label("area = 11", (0,-1), S); label("area = 13", (10,-1), S); [/asy]


$\textbf{(A)}\ 2520 \qquad \textbf{(B)}\ 3150 \qquad \textbf{(C)}\ 3840 \qquad \textbf{(D)}\ 4730 \qquad \textbf{(E)}\ 5050$

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