Worksheet: Polynomial Expressions

In this worksheet, we will practice solving word problems through forming and evaluating polynomial expressions using the information provided in the questions.

Q1:

Find an expression for the area of the shaded region in the figure below.

  • A 8 2 ๐‘ฅ
  • B 7 4 ๐‘ฅ
  • C 7 8 ๐‘ฅ ๏Šจ
  • D 7 4 ๐‘ฅ ๏Šจ
  • E 8 2 ๐‘ฅ ๏Šจ

Q2:

Express the perimeter of the figure below in terms of ๐‘ฅ.

  • A 3 3 ๐‘ฅ length units
  • B 6 6 ๐‘ฅ length units
  • C 4 9 ๐‘ฅ ๏Šจ length units
  • D 5 0 ๐‘ฅ ๏Šจ length units
  • E 2 7 2 ๐‘ฅ length units

Q3:

Write, in the simplest form, an expression that represents the perimeter of the given triangle.

  • A 1 6 ๐‘ฅ + 6
  • B 1 6 ๐‘ฅ โˆ’ 6
  • C 1 6 ๐‘ฅ + 1 0
  • D 1 1 ๐‘ฅ โˆ’ 6
  • E 1 1 ๐‘ฅ + 6

Q4:

The figure below shows a rectangle whose length is 7 cm and width is ๐‘Ž cm. If its perimeter is ๐‘ cm, write a formula for ๐‘ in terms of ๐‘Ž and find the perimeter when ๐‘Ž is 4 cm.

  • A ๐‘ = 2 ( 7 + ๐‘Ž ) , 28 cm
  • B ๐‘ = 7 + ๐‘Ž , 22 cm
  • C ๐‘ = 2 ( 7 + ๐‘Ž ) , 11 cm
  • D ๐‘ = 2 ( 7 + ๐‘Ž ) , 22 cm

Q5:

Write an expression for the total area of the rectangle.

  • A 9 0 ๐‘ฅ ๐‘ฆ square units
  • B ( 1 0 ๐‘ฅ + 9 ๐‘ฆ ) square units
  • C ( 2 0 ๐‘ฅ + 1 8 ๐‘ฆ ) square units
  • D 9 0 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šฉ square units

Q6:

Write an expression for the area of the shaded region in the shape below.

  • A 1 3 1 ๐‘ค + 2 0 ๐‘ค ๏Šจ
  • B 1 2 5 ๐‘ค + 1 6 3 ๐‘ค ๏Šจ
  • C 1 5 2 ๐‘ค + 1 6 3 ๐‘ค ๏Šจ
  • D 1 2 5 ๐‘ค + 1 7 5 ๐‘ค ๏Šจ

Q7:

Find an expression for the area of the shape shown below.

  • A 4 7 ๐‘ฅ ๏Šจ
  • B 4 4 ๐‘ฅ ๏Šจ
  • C 4 3 ๐‘ฅ ๏Šจ
  • D 4 5 ๐‘ฅ ๏Šจ
  • E 2 8 ๐‘ฅ ๏Šจ

Q8:

What is the total shaded area in the figure below?

  • A 6 5 ๐‘Ž ๐‘ + 8 2 ๐‘
  • B 6 5 ๐‘Ž ๐‘ + 8 3 ๐‘
  • C 6 4 ๐‘Ž ๐‘ + 8 3 ๐‘
  • D 6 3 ๐‘Ž ๐‘ + 8 1 ๐‘

Q9:

Write an expression for the area in cm2 of a triangle of height 10๐‘ฅ cm and base 10๐‘ฅ๏Šฉ cm.

  • A 1 0 ๐‘ฅ ๏Šช cm2
  • B 5 0 ๐‘ฅ ๏Šช cm2
  • C 1 0 0 ๐‘ฅ ๏Šช cm2
  • D 5 0 ๐‘ฅ cm2
  • E 5 0 ๐‘ฅ ๏Šฉ cm2

Q10:

A square has sides of length ๐‘™. A new square is formed with double the side length. Find the perimeter ๐‘ƒ and area ๐ด of this new square.

  • A ๐‘ƒ = 2 ๐‘™ , ๐ด = ๐‘™ ๏Šจ
  • B ๐‘ƒ = 6 ๐‘™ , ๐ด = 8 ๐‘™ ๏Šจ
  • C ๐‘ƒ = 1 6 ๐‘™ , ๐ด = 1 6 ๐‘™ ๏Šจ
  • D ๐‘ƒ = 8 ๐‘™ , ๐ด = 4 ๐‘™ ๏Šจ
  • E ๐‘ƒ = 4 ๐‘™ , ๐ด = 2 ๐‘™ ๏Šจ

Q11:

Find an expression for the perimeter of the shape shown below.

  • A 3 3 ๐‘ฅ
  • B 3 1 ๐‘ฅ
  • C 3 2 ๐‘ฅ
  • D 3 8 ๐‘ฅ
  • E 2 1 ๐‘ฅ

Q12:

What is the perimeter of a square whose side length is 40๐‘ฅ cm?

  • A ( 1 6 0 โˆ’ ๐‘ฅ ) cm
  • B ( 1 6 0 + ๐‘ฅ ) cm
  • C 1 6 0 ๐‘ฅ cm
  • D ( 1 6 0 รท ๐‘ฅ ) cm

Q13:

The figure below shows a rectangle whose length is 3 cm and width is ๐‘Ž cm. If its perimeter is ๐‘ cm, write a formula for ๐‘ in terms of ๐‘Ž and find the perimeter when ๐‘Ž is 2 cm.

  • A ๐‘ = 2 ( 3 + ๐‘Ž ) , 6 cm
  • B ๐‘ = 3 + ๐‘Ž , 10 cm
  • C ๐‘ = 2 ( 3 + ๐‘Ž ) , 5 cm
  • D ๐‘ = 2 ( 3 + ๐‘Ž ) , 10 cm

Q14:

Write an expression for the total area of the rectangle.

  • A 4 3 2 ๐‘ฅ ๐‘ฆ square units
  • B ( 1 6 ๐‘ฅ + 2 7 ๐‘ฆ ) square units
  • C ( 3 2 ๐‘ฅ + 5 4 ๐‘ฆ ) square units
  • D 4 3 2 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šฉ square units

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