http://www.ck12.org Chapter 10. Perimeter and Area
a)
Shorter sides of kite Longer sides of kite
62 + 52 =s^21122 + 52 =s^22
36 + 25 =s^21144 + 25 =s^22
s 1 =√
61 s 2 =√
169 = 13
P= 2
(√
61
)
+ 2 ( 13 ) = 2
√
61 + 26 ≈ 41. 6
A=
1
2
( 10 )( 18 ) = 90
b)
Smaller diagonal portion Larger diagonal portion
202 +d^2 s= 252 202 +d^2 l= 352
ds^2 = 225 dl^2 = 825
ds= 15 dl= 5√
33
P= 2 ( 25 )+ 2 ( 35 ) = 120
A=
1
2
(
15 + 5
√
33
)
( 40 )≈ 874. 5
Example 5:The vertices of a quadrilateral areA( 2 , 8 ),B( 7 , 9 ),C( 11 , 2 ), andD( 3 , 3 ). Determine the type of quadri-
lateral and find its area.
Solution:For this problem, it might be helpful to plot the points. From the graph we can see this is probably a kite.
Upon further review of the sides,AB=ADandBC=DC(you can do the distance formula to verify). Let’s see if
the diagonals are perpendicular by calculating their slopes.
mAC=2 − 8
11 − 2
=−
6
9
=−
2
3
mBD=9 − 3
7 − 3
=
6
4
=
3
2
Yes, the diagonals are perpendicular because the slopes are opposite signs and reciprocals.ABCDis a kite. To find
the area, we need to find the length of the diagonals. Use the distance formula.