1. 7-4 Area of Trapezoids, Rhombuses, and Kites
3/10/17
7-4 Area of Trapezoids, Rhombuses, and Kites
Objective: To find the area of a trapezoid, rhombus, or kite.
HEIGHT OF A TRAPEZOID: the perpendicular distance h between the bases
THEOREM AREA OF A TRAPEZOID
The area of a trapezoid is half the product of the height and the sum of the bases.
A = ½ h (b1 + b2) b1 h b2

2. THEOREM 7-11 AREA OF A RHOMBUS OR A KITE
Ex: S 5m R
A = ½ h (b1 + b2)
h A = ½ (2 3)(7 + 5)
60o A = m2
P Q
7 m
THEOREM AREA OF A RHOMBUS OR A KITE
The area of a rhombus or a kite is half the product of the lengths of its diagonals.
A = ½ d1d2
= 2 3 2 d1 d2

3. Ex: Find the area of kite KLMN. KM = 7 and LN = 6
THEOREM AREA OF A KITE OR RHOMBUS
The area of a kite or a rhombus is half the product of the diagonals.
A = ½d1d2
Ex: Find the area of kite KLMN.
KM = 7 and LN = 6
A = ½ d1d2 Area of kite L
A = ½ (7)(6) Substitute m
A = 21 m2 Simplify K 2m m M 3m N
Find the area of a kite with diagonals that are 12 in and 9 in long.
A = ½ (12)(9) = 54 in2

4. Ex: Find the area of rhombus ABCD. 9 15 E 12
Ex: Find the area of rhombus ABCD.
BE = 9 using the Pythagorean triple. Since the diagonals of a rhombus bisect each other,
AC = 24 and BD = 18.
A = ½ d1d Area of rhombus
= ½ (24)(18) Substitute
= 216 m Simplify A D

5. Find the area of Rhombus RSTV R S ST = 13, RT = 24
V T
Find the area of Kite WXYZ Y
X cm cm Z
3 cm W 5 12
A = ½ (24)(10) = 120 13 5 12 3
A = ½ (6)(5) = 15 cm2

6. Find the area of a trapezoid with bases 3 m and 19 m and height 9 m.
A = ½(9)(3 + 19) = 9(11) = 99 m2
Find the area of a trapezoid with bases 3 m and 19 m and height 9 m.
Find the area of a trapezoid in a coordinate plane with vertices at (1,1), (1,6), (5,9), and (5,1).
Find the area. Leave it in simplest radical form.
Trapezoid ABCD
C in D
14 in B
Kite with diagonals 20 m and m long
Rhombus MNOP N
29 mm
M mm O P
A = ½(4)(5 + 8) = 26
A = ½(7 3)( ) = ½
7 3 F
60° A 7
A = ½(20)(10 2) = 20
A = ½(40)(42) = 840 mm2 21

7. Assignment:
Page 376 #2 – 20 even, 27 – 35 odd