Composite Polynomials Worksheet
Algebra I • Polynomial Operations
Composite Figures & Polynomials
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Directions: Determine the perimeter or area for each composite rectangular figure by adding, subtracting, or multiplying polynomials. Show your algebraic work in the space provided, then bubble your answer choice.
Problem 1 Perimeter of an L-Shaped Figure
Find unknown sides • Add polynomials
Find the simplified algebraic expression that represents the total perimeter of the composite figure shown below.
2x + 1 3x + 2 4x + 3 x + 4
A \(10x + 10\)
B \(14x + 10\)
C \(7x + 5\)
D \(14x + 16\)
Workspace
Problem 2 Area of an L-Shaped Figure
Decompose • Multiply & add polynomials
Find the simplified polynomial expression for the total area of the L-shaped figure.
x + 2 2x + 3 3x + 1 x - 1
A \(6x^2 + 11x + 3\)
B \(4x^2 + 10x + 7\)
C \(4x^2 + 4x + 7\)
D \(5x^2 + 5x + 5\)
Workspace
Problem 3 Perimeter of a T-Shaped Figure
Symmetry • Combining like terms
The composite figure is formed by a horizontal crossbar and a vertical stem. What is the total perimeter?
4x + 2 x + 1 2x 3x - 1
A \(10x + 2\)
B \(14x + 2\)
C \(16x + 4\)
D \(18x + 6\)
Workspace
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Composite Figures & Polynomials (Continued)
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Problem 4 Area of a Shaded Border Region
Polynomial subtraction • Distributive law
A smaller rectangular window is cut out of a larger rectangular sheet. Find the area of the shaded region.
CUTOUT 3x + 5 2x + 2 x + 3 x + 1
A \(7x^2 + 20x + 13\)
B \(5x^2 + 12x + 7\)
C \(5x^2 + 20x + 13\)
D \(5x^2 + 12x - 7\)
Workspace
Problem 5 Perimeter of a U-Shaped Channel
Interior boundaries • Polynomial sums
Find the simplified expression for the total perimeter of the U-shaped channel, including all outer and inner edges.
4x + 6 3x + 2 3x + 2 2x x + 1
A \(14x + 16\)
B \(16x + 18\)
C \(14x + 18\)
D \(18x + 20\)
Workspace
Problem 6 Total Area of Two Connected Rectangles
FOIL / Binomial multiplication
The stepped figure consists of two adjacent rectangular blocks placed side-by-side. What is the total combined area?
2x + 1 3x + 4 x + 5 2x - 1
A \(8x^2 + 20x - 1\)
B \(8x^2 + 22x - 1\)
C \(8x^2 + 20x + 9\)
D \(5x^2 + 12x + 3\)
Workspace