Grade 5 Composite Shapes: Area and Perimeter Challenge Worksheet

Student Task

• This worksheet is intended as an extension activity, not a first introduction to area and
• perimeter — students should already be confident with simple rectangles (see the Practice
• Worksheet and Word Problems Worksheet in this collection) before attempting it. Model the
• first shape together on the board, thinking aloud about how the top side relates to the
• bottom side and the notch. Let students work through the remaining shapes independently
• or in pairs, and treat the "Design Your Own" task as an open extension for students who
• finish early rather than a requirement for the whole class.

Classroom Use

• Build It: Using square tiles, cubes, or grid paper, have small groups physically build one
• of the L-shaped figures from the worksheet at a small scale. Groups count the tiles to
• confirm their calculated area, which gives immediate, concrete feedback before they move
• on to the next shape.

Differentiation

Support: Complete Shape 1 as a whole-class or small-group activity before students
attempt Shapes 2 and 3 independently. Provide grid paper so students can count squares to
check their area calculations, and allow a partner to check the missing-side reasoning
before calculating area and perimeter.
On-Level: Students complete all three shapes and the bonus challenge independently, showing their working.
Challenge: Students complete the "Design Your Own" task, and can be asked to create a
composite shape from three rectangles instead of two.

Answer Key & Assessment

Completed worksheet, checked against the answer key, with particular attention to the missing-side reasoning
Observation during the "Build It" activity or paired work
The "Design Your Own" task can be collected as a short extension assessment for early finishers

Learning Objectives

• Students will be able to find a missing side length on a composite rectilinear shape using the lengths of the other sides.
• Students will be able to split a composite shape into two rectangles.
• Students will be able to calculate the total area of a composite shape by adding the areas of its parts.
• Students will be able to calculate the perimeter of a composite shape by adding all of its outer sides.
• Students will be able to create their own composite shape problem with consistent, correct measurements.

Teacher Tips

Give students squared or grid paper alongside this worksheet. Being able to sketch the
dividing line between the two rectangles directly onto (or over) the figure makes the
"split into two rectangles" step far more concrete than working from the printed diagram alone.

What's Included

• 3-page student worksheet (3 composite shapes plus a bonus challenge shape and a design task)
• Fully worked answer key showing the missing-side reasoning and the rectangle split for every shape
• Editable DOCX version of the worksheet and the answer key
• Print-ready PDF of the worksheet
• Print-ready PDF answer key

Additional Files

• Composite Shapes.docx
• Answer Key (Printable)

Teacher Reviews