Lesson 11
Grade 10
Name: _______________________________________ Period: ________ Date:_________
Activity: Area of Shaded Regions in Terms of x
The largest rectangle below has been divided into four smaller nonoverlapping rectangular
regions as shown.
1. Determine and record the area of each region on the drawing below.
4x
7
Area of Region A
Area of
Region B
Area of Region C
Area of
Region D
x
5
2. In terms of x, what is the area of the largest rectangle?
A = lw
A=(
)(
)
A=
3. Use subtraction to write an expression for the combined area of regions A and C using your
expression for the area of the largest rectangle and the areas of regions B and D.
4. Write an expression for the area of the unshaded portion of the rectangle if the area of the
shaded portion is 50 square feet.
x+5
x
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Lesson 11
Grade 10
5. What is the area of the rectangle shown below?
8x2y
A = lw
A=(
10xy
)(
)
A=
6. The area of the shaded portion of the rectangle is 10x3y2. Write an expression for the
unshaded portion.
12x2y
A (unshaded) = A (largest) – A (shaded)
7xy
A=(
)(
A=(
)–(
)–(
)
)
A=
7. What is the length of the rectangle shown below?
A = lw
6xy
Area = 42x2y5
(
)=l(
)
l=
8. The largest rectangle below has been divided into four smaller nonoverlapping rectangular
regions. The area of each region is shown. What is the length of the largest rectangle?
x
x2
3x
4
4x
12
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Lesson 11
Grade 10
9. The largest rectangle below has been divided into four smaller nonoverlapping rectangular
regions. The area of each region is shown. Determine the length and width of the largest
rectangle.
x2
9x
3x
27
10. The trinomial 3 x 2 − 11x − 20 represents the area of a rectangle. If the binomial x – 5
represents the width of the rectangle, what binomial would represent the length of the
rectangle?
11. The length of a rectangle is x2 and its width is x. Write an expression that represents the
area of the rectangle then raise the area to the 5th power.
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Lesson 11
Grade 10
Name: ______________________________________ Period: ________
Date: ________
Activity: Area of Regions
1. The largest rectangle below is divided into two smaller rectangular regions. The area
of the unshaded region is 25 square inches. Write an expression that represents the
area of the shaded portion of the largest rectangle.
(2x – 4) inches
(3x + 3)
inches
2. The largest rectangle below is divided into three smaller rectangular regions. The
area of each shaded region is 15 square inches. Write an expression that represents
the area of the unshaded portion of the largest rectangle.
6mn3 inches
7m2n inches
3. The largest rectangle below is divided into a square and a smaller rectangular
region. The area of the unshaded region is 14 square inches. Write an expression
that represents the area of the largest rectangle.
(2a – 3) inches
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Lesson 11
Grade 10
4. What is the area of a rectangle with a length of 9a 2b3 units and width of 4ab 4 units?
5. What is the area of a rectangle with a length of 3x + 2 units and width of 5x + 1
units?
6. The area of a rectangle is 10 xy 4 square units. If the length of the rectangle is 5 y 2
units, how many units wide is the rectangle?
7. The trinomial 6 x 2 + 17 x + 12 represents the area of a rectangle. If the binomial 3x + 4
represents the length of the rectangle, what binomial would represent the width of
the rectangle?
8. The area of a square is x10. What is the length of one side of the square?
9. Simplify the expression ( a 2 ) .
6
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© 2007 Region 4 Education Service Center
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Lesson 11
Grade 10
Name: ___________________________________________ Period: __________ Date: _________
Evaluate: Area Models
1
Which expression best represents
the area of the rectangle below?
3
x+4
x+2
A x2 + 8
B x2 + 6x + 8
Joseph was asked to find an
expression that is equivalent to x 8 .
Which of the following is
equivalent to x8 ?
A
(x )
B
(x )
C
(x )
D
(x )
C 2x + 6
6 2
4 4
4 2
2 6
D x2 + 8x + 6
4
2
The area of a rectangle is 72x 3 y 4 . If
the width of the rectangle is 8xy 3 ,
what is the length of the rectangle?
The area of the shaded portion of
the largest rectangle is 80 square
feet.
x+7
x
3
A 9x y
B 9x3 y 2
How can the area of the unshaded
portion be expressed in terms of x?
C 9x 2 y 2
D 9x 2 y
A x 2 + 7 x − 80
B 7 x − 80
C
x 2 − 80
D 2 x + 7 − 80
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