1994 AMC 12 Problem 7

Attempt Problem 7 of the 1994 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Squares

ABCD

and

EFGH

are congruent,

AB=10,

and

G

is the center of square

ABCD.

The area of the region in the plane covered by these squares is

75

100

125

150

175

The overlap is triangle

GAB

The distance from the center

G

to side

\overline{AB}

5

Each square has area

100.

Their overlap is

\triangle GAB,

whose base is

AB=10

and whose altitude from the center

G

\overline{AB}

5.

Its area is

\frac12(10)(5)=25.

Hence the union has area

100+100-25=175.

Thus the correct answer is E.

Problem 7 in other years