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.

  • A82๐‘ฅ
  • B74๐‘ฅ
  • C78๐‘ฅ๏Šจ
  • D74๐‘ฅ๏Šจ
  • E82๐‘ฅ๏Šจ

Q2:

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

  • A33๐‘ฅ length units
  • B66๐‘ฅ length units
  • C49๐‘ฅ๏Šจ length units
  • D50๐‘ฅ๏Šจ length units
  • E272๐‘ฅ length units

Q3:

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

  • A16๐‘ฅ+6
  • B16๐‘ฅโˆ’6
  • C16๐‘ฅ+10
  • D11๐‘ฅโˆ’6
  • E11๐‘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.

  • A๐‘=2(7+๐‘Ž), 28 cm
  • B๐‘=7+๐‘Ž, 22 cm
  • C๐‘=2(7+๐‘Ž), 11 cm
  • D๐‘=2(7+๐‘Ž), 22 cm

Q5:

Write an expression for the total area of the rectangle.

  • A90๐‘ฅ๐‘ฆ square units
  • B(10๐‘ฅ+9๐‘ฆ) square units
  • C(20๐‘ฅ+18๐‘ฆ) square units
  • D90๐‘ฅ๐‘ฆ๏Šฉ๏Šฉ square units

Q6:

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

  • A131๐‘ค+20๐‘ค๏Šจ
  • B125๐‘ค+163๐‘ค๏Šจ
  • C152๐‘ค+163๐‘ค๏Šจ
  • D125๐‘ค+175๐‘ค๏Šจ

Q7:

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

  • A47๐‘ฅ๏Šจ
  • B44๐‘ฅ๏Šจ
  • C43๐‘ฅ๏Šจ
  • D45๐‘ฅ๏Šจ
  • E28๐‘ฅ๏Šจ

Q8:

What is the total shaded area in the figure below?

  • A65๐‘Ž๐‘+82๐‘
  • B65๐‘Ž๐‘+83๐‘
  • C64๐‘Ž๐‘+83๐‘
  • D63๐‘Ž๐‘+81๐‘

Q9:

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

  • A10๐‘ฅ๏Šช cm2
  • B50๐‘ฅ๏Šช cm2
  • C100๐‘ฅ๏Šช cm2
  • D50๐‘ฅ cm2
  • E50๐‘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.

  • A๐‘ƒ=2๐‘™, ๐ด=๐‘™๏Šจ
  • B๐‘ƒ=6๐‘™, ๐ด=8๐‘™๏Šจ
  • C๐‘ƒ=16๐‘™, ๐ด=16๐‘™๏Šจ
  • D๐‘ƒ=8๐‘™, ๐ด=4๐‘™๏Šจ
  • E๐‘ƒ=4๐‘™, ๐ด=2๐‘™๏Šจ

Q11:

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

  • A33๐‘ฅ
  • B31๐‘ฅ
  • C32๐‘ฅ
  • D38๐‘ฅ
  • E21๐‘ฅ

Q12:

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

  • A(160โˆ’๐‘ฅ) cm
  • B(160+๐‘ฅ) cm
  • C160๐‘ฅ cm
  • D(160รท๐‘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.

  • A๐‘=2(3+๐‘Ž), 6 cm
  • B๐‘=3+๐‘Ž, 10 cm
  • C๐‘=2(3+๐‘Ž), 5 cm
  • D๐‘=2(3+๐‘Ž), 10 cm

Q14:

Write an expression for the total area of the rectangle.

  • A432๐‘ฅ๐‘ฆ square units
  • B(16๐‘ฅ+27๐‘ฆ) square units
  • C(32๐‘ฅ+54๐‘ฆ) square units
  • D432๐‘ฅ๐‘ฆ๏Šฉ๏Šฉ square units

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