LESSON 11 –2

Five-Minute Check (over Lesson 11 –1)
Then/Now
New Vocabulary
Key Concept: Area of a Trapezoid
Example 1: Real-World Example: Area of a Trapezoid
Example 2: Area of a Trapezoid
Key Concept: Area of a Rhombus or Kite
Example 3: Area of a Rhombus and a Kite
Example 4: Use Area to Find Missing Measures
Concept Summary: Areas of Polygons

Over Lesson 11 –1
Find the perimeter of the figure. Round to the nearest tenth if necessary.
A.
48 cm
B.
56 cm
C.
101.1 cm
D.
110 cm

Over Lesson 11 –1
Find the perimeter of the figure. Round to the nearest tenth if necessary.
A.
37.9 ft
B.
40 ft
C.
43.9 ft
D.
45 ft

Over Lesson 11 –1
Find the area of the figure. Round to the nearest tenth if necessary.
A.
58 in 2
B.
83 in
2
C.
171.5 in
2
D.
180 in
2

Over Lesson 11 –1
Find the area of the figure. Round to the nearest tenth if necessary.
A.
9.0 m 2
B.
62 m
2
C.
5 m 2
D.
3.4 m
2

Over Lesson 11 –1
Find the height and base of the parallelogram if the area is
168 square units.
A.
11 units; 13 units
B.
12 units; 14 units
C.
13 units; 15 units
D.
14 units; 16 units

Over Lesson 11 –1
The area of an obtuse triangle is 52.92 square centimeters. The base of the triangle is 12.6 centimeters. What is the height of the triangle?
A.
2.1 centimeters
B.
4.2 centimeters
C.
8.4 centimeters
D.
16.8 centimeters

You found areas of triangles and parallelograms.
• Find areas of trapezoids.
• Find areas of rhombi and kites.

• height of a trapezoid

Area of a Trapezoid
SHAVING Find the area of steel used to make the side of the razor blade shown below.
Answer: A = 2.75 cm
2
Area of a trapezoid h = 1, b
1
= 3, b
2
= 2.5
Simplify.

Find the area of the side of the pool outlined below.
A.
288 ft
2
B.
295.5 ft
2
C.
302.5 ft
2
D.
310 ft
2

Area of a Trapezoid
OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck.
Read the Item
You are given a trapezoid with one base measuring
4 feet, a height of 9 feet, and a third side measuring
5 feet. To find the area of the trapezoid, first find the measure of the other base.

Area of a Trapezoid
Solve the Item
Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of
4 feet and a width of x feet.

Area of a Trapezoid
Use the Pythagorean Theorem to find ℓ.
a
2
+ b
2
= c
2
4
2
+ ℓ 2
= 5
2
16 + ℓ 2
= 25 ℓ 2
= 9 ℓ = 3
Pythagorean Theorem
Substitution
Simplify.
Subtract 16 from each side.
Take the positive square root of each side.

Area of a Trapezoid
By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid.
Area of a trapezoid
Substitution
Simplify.
Answer: So, the area of the deck is 30 square feet.

Area of a Trapezoid
Check
The area of the trapezoid is the sum of the areas of the areas of the right triangle and rectangle. The area of the triangle is or 6 square feet. The area of the rectangle is (4)(6) or 24 square feet. So, the area of the trapezoid is 6 + 24 or 30 square feet.

Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed.
A.
58 ft 2
B.
63 ft
2
C.
76 ft
2
D.
88 ft
2

Area of a Rhombus and a Kite
A. Find the area of the kite.
Area of a kite d
1
= 7 and d
2
= 12
Answer: 42 ft
2

Area of a Rhombus and a Kite
B. Find the area of the rhombus.
Step 1 Find the length of each diagonal.
Since the diagonals of a rhombus bisect each other, then the lengths of the diagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in.

Area of a Rhombus and a Kite
Step 2 Find the area of the rhombus.
Area of a rhombus
2 d
1
= 14 and d
2
= 18
Simplify.
Answer: 126 in 2

A.
Find the area of the kite.
A.
48.75 ft 2
B.
58.5 ft
2
C.
75.25 ft 2
D.
117 ft
2

B.
Find the area of the rhombus.
A.
45 in
2
B.
90 in
2
C.
180 in 2
D.
360 in
2

Use Area to Find Missing Measures
ALGEBRA One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square inches, what are the lengths of the diagonals?
Step 1 Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other
1 x .
2

Use Area to Find Missing Measures
Step 2 Use the formula for the area of a rhombus to find x .
Area of a rhombus
256 =
16 = x x
2
A = 64, d
1
= x , d
2
1 x
2
Simplify.
Multiply each side by 4.
Take the positive square root of each side.

Use Area to Find Missing Measures
Answer: So, the lengths of the diagonals are 16 inches and (16) or 8 inches.
2

Trapezoid QRST has an area of 210 square yards.
Find the height of QRST.
A.
3 yd
B.
6 yd
C.
2.1 yd
D.
7 yd

LESSON 11 –2