1. A = h(b1 + b2) Area of a trapezoid
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
A car window is shaped like the trapezoid shown. Find the area of the window.
A = h(b1 + b2) Area of a trapezoid 1 2
A = (18)( ) Substitute 18 for h, 20 for b1, and 36 for b2. 1 2
A = Simplify.
The area of the car window is 504 in.2
Quick Check

2. Find the area of trapezoid ABCD.
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
Find the area of trapezoid ABCD.
Draw an altitude from vertex B to DC that divides trapezoid ABCD
into a rectangle and a right triangle.
Because opposite sides of rectangle ABXD
are congruent, DX = 11 ft and
XC = 16 ft – 11 ft = 5 ft.

3. Taking the square root, BX = 12 ft. You may remember
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
(continued)
By the Pythagorean Theorem, BX 2 + XC2 = BC2, so BX 2 = 132 – 52 = 144.
Taking the square root, BX = 12 ft. You may remember
that 5, 12, 13 is a Pythagorean triple.
A = h(b1 + b2) Use the trapezoid area formula. 1 2
A = (12)( ) Substitute 12 for h, 11 for b1, and 16 for b2. 1 2
A = Simplify.
The area of trapezoid ABCD is 162 ft2.
Quick Check

4. Find the area of kite XYZW.
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
Find the area of kite XYZW.
Find the lengths of the diagonals of kite XYZW.
XZ = d1 = = 6 and YW = d2 = = 5
A = d1d2 Use the formula for the area of a kite. 1 2
A = (6)(5) Substitute 6 for d1 and 5 for d2. 1 2
A = 15 Simplify.
The area of kite XYZW is 15 cm2.
Quick Check

5. Find the area of rhombus RSTU.
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
Find the area of rhombus RSTU.
To find the area, you need to know the lengths of both diagonals.
Draw diagonal SU, and label the intersection of the diagonals point X.

6. SXT is a right triangle because the diagonals of
Areas of Trapezoids, Rhombuses, and Kites
LESSON 10-2
Additional Examples
(continued)
SXT is a right triangle because the diagonals of
a rhombus are perpendicular.
The diagonals of a rhombus bisect each other, so TX = 12 ft.
You can use the Pythagorean triple 5, 12, 13 or the Pythagorean Theorem
to conclude that SX = 5 ft.
SU = 10 ft because the diagonals of a rhombus bisect each other.
A = d1d2 Area of a rhombus 1 2
A = (24)(10) Substitute 24 for d1 and 10 for d2. 1 2
A = Simplify.
Quick Check
The area of rhombus RSTU is 120 ft2.