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Special Right Triangles and Area

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45°- 45° - 90°

30° - 60° - 90°

Trapezoid

Kite

Rhombus

10

10

10

10

10

20

20

20

20

20

30

30

30

30

30

40

40

40

40

50

50

50

Special Right Triangles and Area

In triangle ABC, is a right angle and 45°. Find BC. If you answer is not an integer, leave it in simplest radical form.

Find the length of the hypotenuse.

Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

Find the lengths of the missing sides in the triangle.

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

60°

8

x

30°

y

Find the value of each variable.

Shorter Leg

8 = 2x

x = 4

Longer Leg

y = x√3

y = 4√3

Find the lengths of a 30°-60°-90° triangle with hypotenuse of length 12.

60°

12

x

30°

y

Shorter Leg

12 = 2x

x = 6

Longer Leg

y = x√3

y = 6√3

The longer leg of a 30°-60°-90° has length 18. Find the length of the shorter leg and the hypotenuse.

30°

60°

18

x

y

Shorter Leg

Hypotenuse

Find the area of the trapezoid. Leave your answer in simplest radical form.

5cm

h

60°

7cm

Find area.

Find h.

Find the area of the trapezoid. Leave your answer in simplest radical form.

11cm

h

60°

16cm

Find h.

Find area.

A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?

Find the area of kite KLMN.

L

3m

2m

M

K

5m

3m

KM=2+5=7

LN=3+3=6

N

Find the area of kite KLMN.

L

3m

1m

M

K

4m

3m

KM=1+4=5

LN=3+3=6

N

Find the area of kite with diagonals that are 12 in. and 9 in. long.

Find the area of the rhombus.

B

Find the area of rhombus ABCD.

15m

E

A

C

12m

D

AC=12+12=24

BD=9+9=18

Find the area of rhombus ABCD.

B

13m

24m

E

A

C

12m

12m

D

AC=12+12=24

BD=5+5=10