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Five-Minute Check (over Lesson 111) CCSS Then/Now
New Vocabulary Key Concept Area of a
Trapezoid Example 1 Real-World Example Area of
a Trapezoid Example 2 Standardized Test Example
Area of a Trapezoid Key Concept Area of a
Rhumbus or Kite Example 3 Area of a Rhombus and
a Kite Example 4 Use Area to Find Missing
Measures Concept Summary Areas of Polygons
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5-Minute Check 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
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5-Minute Check 2
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
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5-Minute Check 3
Find the area of the figure. Round to the
nearest tenth if necessary.
A. 58 in2 B. 83 in2 C. 171.5 in2 D. 180 in2
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5-Minute Check 4
Find the area of the figure. Round to the
nearest tenth if necessary.
A. 9.0 m2 B. 62 m2 C. 5 m2 D. 3.4 m2
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5-Minute Check 5
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
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5-Minute Check 6
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
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CCSS
Content Standards G.MG.3 Apply geometric methods
to solve problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost working with typographic grid
systems based on ratios). Mathematical
Practices 1 Make sense of problems and persevere
in solving them. 7 Look for and make use of
structure.
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Then/Now
You found areas of triangles and parallelograms.

• Find areas of trapezoids.

• Find areas of rhombi and kites.

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Vocabulary

• height of a trapezoid

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Concept 1
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Example 1
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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Example 1
Find the area of the side of the pool outlined
below.
A. 288 ft2 B. 295.5 ft2 C. 302.5 ft2 D. 310 ft2
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Example 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 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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Example 2
Area of a Trapezoid
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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Example 2
Area of a Trapezoid
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 root of each side.
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Example 2
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.
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Example 2
Area of a Trapezoid
Check
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Example 2
Ramon is carpeting a room shaped like the
trapezoid shown below. Find the area of the
carpet needed.
A. 58 ft2 B. 63 ft2 C. 76 ft2 D. 88 ft2
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Concept 2
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Example 3A
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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Example 3B
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.
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Example 3B
Area of a Rhombus and a Kite
Step 2 Find the area of the rhombus.
Area of a rhombus
d1 14 and d2 18
Answer 126 in2
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Example 3A
A. Find the area of the kite.
A. 48.75 ft2 B. 58.5 ft2 C. 75.25 ft2 D. 117 ft2
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Example 3B
B. Find the area of the rhombus.
A. 45 in2 B. 90 in2 C. 180 in2 D. 360 in2
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Example 4
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?
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Example 4
Use Area to Find Missing Measures
Step 2 Use the formula for the area of a rhombus
to find x.
Area of a rhombus
Simplify.
256 x2 Multiply each side by 4.
16 x Take the positive square root of each
side.
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Example 4
Use Area to Find Missing Measures
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Example 4
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
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Concept 3
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End of the Lesson