Special Right Triangles and Area
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Special Right Triangles and Area
50505040404040
303030303020202020201010101010
RhombusKiteTrapezoid30° - 60° - 90°
45°- 45° - 90°
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In triangle ABC, is a right angle and 45°. Find BC. If you answer is not an integer, leave it in simplest radical form.
211112
2.
xx
leghyp
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Find the length of the hypotenuse.
62343
2322.
xxxx
leghyp
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Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
x
x
x
x
xleghyp
282
21622
2162
16216
2.
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Find the lengths of the missing sides in the triangle.
7
2772
2.
y
xx
leghyp
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Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
x
x
x
xleghyp
225
22
2525
252.
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3663
3
xx
SLLL
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yy
SLhyp
3102320
2.
303103
3
xx
SLLL
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Find the value of each variable.
60°
30°x
y
8 Shorter Leg8 = 2xx = 4
Longer Legy = x√3y = 4√3
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Find the lengths of a 30°-60°-90° triangle with hypotenuse of length 12.
60°
30°
y
x12
Shorter Leg12 = 2x
x = 6
Longer Legy = x√3y = 6√3
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30°
60°
18
xy Shorter
Leg x 318
318
x
33
318
x
Hypotenuse 362 y
312y
The longer leg of a 30°-60°-90° has length 18. Find the length of the shorter leg and the hypotenuse.
3318
x
36x
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2
21
66.303
)32.607(21
)2.48)(6.12(21
)2.2919)(6.12(21
)(21
inA
A
A
A
bbhA
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2
21
70
)140(21
)20)(7(21
)128)(7(21
)(21
inA
A
A
A
bbhA
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SLSL
SLhyp
428
2.
3443
3
LLLL
SLLL
332
)364(21
)16)(34(21
)106)(34(21
)(21
21
A
A
A
A
bbhA
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Find the area of the trapezoid. Leave your answer in simplest radical form.
7cm7cm)(21
21 bbhA
hh
Find h. SLLL 3
23 h32h
Find area. )57)(32(2
1A
)12)(32(21
A
)12)(31(A2312 cmA
60°60°
5cm5cm
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Find the area of the trapezoid. Leave your answer in simplest radical form.
16cm16cm)(21
21 bbhA
hh
Find h. SLLL 3
53 h35h
Find area. )1611)(35(2
1A
)27)(35(21
A
)27)(35.2(A235.67 cmA
60°60°
11cm11cm
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A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?
8.36)6.73(2
1)8)(2.9(2
121
21
A
A
A
ddA
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Find the area of kite KLMN.
2m5m
3m
3mKK
LL
MM
NN
KM=2+5=7LN=3+3=6
2121 ddA
)6)(7(21
A
)42(21
A
221mA
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Find the area of kite KLMN.
1m4m
3m
3mKK
LL
MM
NNKM=1+4=5LN=3+3=6
2121 ddA
)6)(5(21
A
)30(21
A
215mA
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Find the area of kite with diagonals that are 12 in. and 9 in. long.
2121 ddA
)9)(12(21
A
)108(21
A
254mA
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Find the area of the rhombus.Find the area of the rhombus.
128)256(2
1)16)(16(2
121
21
A
A
A
ddA
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Find the area of rhombus ABCD. 15m
12mAA
BB
CC
DD
2121 ddA
)24)(18(21
A
)432(21
A
2216mA
EE
222 cba 222 1512 b
225144 2 b812 b
812 b9b
AC=12+12=2424BDBD=9+9=1818
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Find the area of rhombus ABCD. 13m
24mAA
BB
CC
DD212
1 ddA
)24)(10(21
A
)240(21
A
2120mA
222 cba 222 1312 b
169144 2 b252 b
252 b5b
AC=12+12=2424BDBD=5+5=1010
12m 12mEE
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