10.  Make   two    parallelograms,    differing   very   much   in
shape,  but  having  the  same  area.
11.  Construct  a  parallelogram,  and  then  find  its  area.
12.  The  bases  of  two  parallelograms  are  each  9|  in.  long.
The  altitude  of  one  is  1  in.,  and  the  altitude  of  the  other
is  3  in.     How  much  greater  is  the  area  of  one  than  the  area
of  the  other?

13.  The  bases  of  two  parallelograms  are  equal ;  the  alti-
tude of  one  is  three  times  that  of  the  other.     Compare  their
areas.     Draw  a  figure  to  illustrate  your  answer.
14.  The  altitudes  of  two  parallelograms  are  equal ;    the
base  of  one  is  three  times  that  of  the  other.     Compare  their
areas.     Draw  a  figure  to  illustrate  your  answer.
15.  Find  the  area  of  a  rhombus,  the  perimeter  of  which  is
156  ft.,  and  the  altitude  9  ft.  4  in.
16.  The  area  of  a  field  having  the  shape  of  a  rhombus  is
exactly  10  acres.     The  distance  from  any  one  side  to  the
opposite  side  is  400  ft.     Required  the  cost  of  fencing  the
field  at  $2.50  per  rod.
120


LESSONS   IN  GEOMETRY.
Lesson  63.
1,  Problem.  —  To  find  the  area  of  a  triangle.
Let  ABC  (Fig.  123)  be  a  triangle,  AB  the  base,  CD  the
altitude.
Draw  AE  \\  to  BC,  and  CE  II  to  AB ;  the  figure  ABCE  is
a  parallelogram  having  AB  for  base,  CD  for  altitude.
Therefore,  A  ABC  =  A  AEC   (p.  84,  No.  3).
Hence,    area  of  A  ABC  —  %  area  of  parallelogram  ABCD.
Now,       area  of  parallelogram  ABCD  =  AB  x  CD.
Hence,    area  of  A  ABC  =  %AB  x  CD  ;  or,

Area  of  a  triangle  =  %  x  base  x  altitude.
FIG.  123.
