special right triangles and area
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Special Right Triangles and Area
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RhombusKiteTrapezoid30° - 60° - 90°
45°- 45° - 90°
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
Find the length of the hypotenuse.
62343
2322.
xxxx
leghyp
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.
Find the lengths of the missing sides in the triangle.
7
2772
2.
y
xx
leghyp
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.
3663
3
xx
SLLL
yy
SLhyp
3102320
2.
303103
3
xx
SLLL
Find the value of each variable.
60°
30°x
y
8 Shorter Leg8 = 2xx = 4
Longer Legy = x√3y = 4√3
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
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
2
21
66.303
)32.607(21
)2.48)(6.12(21
)2.2919)(6.12(21
)(21
inA
A
A
A
bbhA
2
21
70
)140(21
)20)(7(21
)128)(7(21
)(21
inA
A
A
A
bbhA
SLSL
SLhyp
428
2.
3443
3
LLLL
SLLL
332
)364(21
)16)(34(21
)106)(34(21
)(21
21
A
A
A
A
bbhA
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
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
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
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
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
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
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
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
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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