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Over Lesson 11–1
A. A
B. B
C. C
D. D
48 cm
Find the perimeter of the figure. Round
to the nearest tenth if necessary.
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Over Lesson 11–1
A. A
B. B
C. C
D. D
37.9 ft
Find the perimeter of the figure. Round
to the nearest tenth if necessary.
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Over Lesson 11–1
A. A
B. B
C. C
D. D
171.5 in2
Find the area of the figure. Round to the nearest tenth if necessary.
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Over Lesson 11–1
A. A
B. B
C. C
D. D
3.4 m2
Find the area of the figure. Round to the nearest tenth if necessary.
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Over Lesson 11–1
A. A
B. B
C. C
D. D
12 units; 14 units
Find the height and base of the parallelogram if the area is 168 square units.
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Over Lesson 11–1
A. A
B. B
C. C
D. D
8.4 centimeters
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?
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• Find areas of trapezoids.
• Find areas of rhombi and kites.
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Area of a Trapezoid
SHAVING Find the area of steel used to make the side of the razor blade shown below.
Area of a trapezoid
h = 1, b1 = 3, b2 = 2.5
Simplify.
Answer: A = 2.75 cm2
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A. A
B. B
C. C
D. D
302.5 ft2
Find the area of the side of the pool outlined below.
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OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck.
Read the Test 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.
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Solve the Test 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.
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Use the Pythagorean Theorem to find ℓ.
a2 + b2 = c2 Pythagorean Theorem
42 + ℓ2 = 52 Substitution
16 + ℓ2 = 25 Simplify.
ℓ2 = 9 Subtract 16 from each side.
ℓ = 3 Take the positive square rootof each side.
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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.
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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.
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A. A
B. B
C. C
D. D
88 ft2
Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed.
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Area of a Rhombus and a Kite
A. Find the area of the kite.
Area of a kite
d1 = 7 and d2 = 12
Answer: 42 ft2
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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 bisecteach other, then the lengths of thediagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in.
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Area of a Rhombus and a Kite
Answer: 126 in2
Area of a rhombus
Step 2 Find the area of the rhombus.
d1 = 14 and d2 = 18
Simplify.2
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A. A
B. B
C. C
D. D
58.5 ft2
A. Find the area of the kite.
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A. A
B. B
C. C
D. D
180 in2
B. Find the area of the rhombus.
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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 diagonal is x.__1
2
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• Does the Rhombus Formula work for a Square?
• s = 4
• d = ?
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Use Area to Find Missing Measures
Step 2 Use the formula for the area of a rhombus to find x.
Area of a rhombus
A = 64, d1= x, d2 = x__12
Simplify.
256 = x2 Multiply each side by 4.
16 = x Take the positive square root of each side.
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Use Area to Find Missing Measures
Answer: So, the lengths of the diagonals are 16 inches
and (16) or 8 inches. __12
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A. A
B. B
C. C
D. D
6 yd
Trapezoid QRST has an area of 210 square yards. Find the height of QRST.