Over Lesson 11–1 A.A B.B C.C D.D 5-Minute Check 1 48 cm Find the perimeter of the figure. Round to...
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Transcript of Over Lesson 11–1 A.A B.B C.C D.D 5-Minute Check 1 48 cm Find the perimeter of the figure. Round to...
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.
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.
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.
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.
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.
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?
• Find areas of trapezoids.
• Find areas of rhombi and kites.
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
A. A
B. B
C. C
D. D
302.5 ft2
Find the area of the side of the pool outlined below.
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.
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.
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.
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.
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.
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.
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
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.
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
A. A
B. B
C. C
D. D
58.5 ft2
A. Find the area of the kite.
A. A
B. B
C. C
D. D
180 in2
B. Find the area of the rhombus.
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
• Does the Rhombus Formula work for a Square?
• s = 4
• d = ?
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.
Use Area to Find Missing Measures
Answer: So, the lengths of the diagonals are 16 inches
and (16) or 8 inches. __12
A. A
B. B
C. C
D. D
6 yd
Trapezoid QRST has an area of 210 square yards. Find the height of QRST.