MathDB

1

Part of 2014-2015 SDML (Middle School)

Problems(2)

Shaded figure in grid

Source: 2014-2015 SDML Middle School 1a Problem 1

8/28/2016
Given that each unit square in the grid below is a 1×11\times1 square, find the area of the shaded region in square units.
[asy] fill((3,0)--(4,0)--(6,3)--(4,4)--(4,3)--(0,2)--(2,2)--cycle, grey); draw((0,0)--(6,0)); draw((0,1)--(6,1)); draw((0,2)--(6,2)); draw((0,3)--(6,3)); draw((0,4)--(6,4)); draw((0,0)--(0,4)); draw((1,0)--(1,4)); draw((2,0)--(2,4)); draw((3,0)--(3,4)); draw((4,0)--(4,4)); draw((5,0)--(5,4)); draw((6,0)--(6,4)); [/asy]
(A) 8(B) 9(C) 10(D) 11(E) 12\text{(A) }8\qquad\text{(B) }9\qquad\text{(C) }10\qquad\text{(D) }11\qquad\text{(E) }12
geometry
Sum of 10 consecutive integers

Source: 2014-2015 SDML Middle School 1b Problem 1

8/28/2016
The sum of 1010 consecutive integers is 7575. What is the smallest of these 1010 integers?