Honors Geometry 1. Homework Answers for Section 11.4 Find the area of a kite with diagonals 6 and 20
6
A=
=
20
1
2
1
2
(d1)(d2)
(20)(6) = 60 u2
2. Find the area of each kite.
a.
5
4
9
A=
1
(8)(14) = 56 u2
2
A=
1
(10)(17) = 85 u2
2
4
b.
13
5
13
c.
16
30°
A=
1
2
(20)(16) = 160 u2
16
20
Baroody Page 1 of 4 Honors Geometry 3. Homework Answers for Section 11.4 The area of a kite is 20. The longer diagonal is 8. Find the shorter diagonal.
A=
20 =
1
2
(d1)(d2)
1
(8)(d2)
2
40 = 8(d2)
5 = d2
. 4. Find the area of the kite shown.
17
10
A=
8
6
15
=
1
(d1)(d2)
2
1
(16)(21) = 168 u2
2
5. Find the area of each rhombus.
a.
b.
25
25
7
24
20
A=
1
(d1)(d2)
2
A = bh
1
= (14)(48) = 336 u2
2
Baroody = (20)(25) = 500 u2
Page 2 of 4 Honors Geometry 6. Homework Answers for Section 11.4 If ABCD is a kite with ∠BAD a right ∠ and BD = 10, find the area of ABCD.
B
13
5
A=
5
A
12
C
=
5
1
2
1
2
(d1)(d2)
(17)(10) = 85 u2
D
7. Find the area of the kite shown.
Using the Altitude-on-Hypotenuse Theorem,
x2 = (4)(9) = 36
x
4
x = 6 (why not -6?)
9
Now,
x
A=
=
1
(d1)(d2)
2
1
(12)(13) = 78 u2
2
8. Find the area of a rhombus with a perimeter of 40 and one angle of 60°.
10
Now,
10
A = bh
5 3
= (10)(5 3 ) = 50 3 u2
60°
5
Baroody Page 3 of 4 Honors Geometry 9. Homework Answers for Section 11.4 a. Find the areas of region I, region II, and region III.
b. Find the area of
OBD
AI =
1
2
AII =
E (0, 7)
D (8, 7)
C (12, 7)
AIII =
B (12, 3)
A
I
II
O (0, 0)
1
(7)(8) = 28 u2
2
1
2
OBD
III
(4)(4) = 8 u2
(12)(3) = 18 u2
= AOECA - (AI + AII + AIII)
= (12)(7) - (8 + 28 + 18)
A (12, 0)
= 84 - 54 = 30 u2
10. Given a rhombus with diagonals 18 and 24, find the height.
15
A=
9
1
1
(d1)(d2) = (18)(24) = 216 u2
2
2
12
A = bh
h
216 = (15)(h)
h=
Baroody 216
72
=
u
15
5
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