10.6. Area and Perimeter of Rhombuses and Kites http://www.ck12.org
- Find the area of a rhombus with diagonals of 6 in and 8 in.
Answers:
In a kite, there are two pairs of congruent triangles. You will need to use the Pythagorean Theorem in both problems
to find the length of sides or diagonals.
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
2.
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
- The area is^12 ( 8 )( 6 ) = 24 in^2.
Interactive Practice
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/113020Explore More
- Do you think all rhombi and kites with the same diagonal lengths have the same area?Explainyour answer.
- Use this picture of a rhombus to show that the area of a rhombus is equal to the sum of the areas of the four
congruent triangles. Write a formula and reduce it to equal^12 d 1 d 2.