Area & Perimeter Worksheet (With Composite Shapes)
Goal: Find the area and perimeter of common shapes, explain how area and perimeter differ, and find the area of a composite figure by adding and subtracting parts.
What to do
- Open the area calculator. Keep “Length unit” on centimeters and the “Area & perimeter” tab selected.
- For each shape in the table, choose it in “Shape”, enter its dimensions and record the results. Draw a dash where the calculator gives no perimeter.
- Scroll down to the composite shape calculator. Its starting L-shape adds a 10 × 6 rectangle and subtracts a 4 × 3 corner. Record the total area.
- Change the second part from “Subtract” to “Add”, choose “Semicircle” as its shape and enter a radius of 3. This makes a 10 × 6 rectangle with a rounded end. Record the total area.
Record your results
| Setting | Area | Perimeter or circumference |
|---|---|---|
| Rectangle: width 8, height 5 | ||
| Rectangle: width 12, height 1 | ||
| Triangle: base 8, height 5 | ||
| Trapezoid: parallel sides 8 and 5, height 4 | ||
| Circle: radius 5 | ||
| Composite: L-shape | ||
| Composite: rectangle + semicircle |
Questions
The two rectangles have the same perimeter. Do they have the same area? What does this tell you?
Compare the triangle (base 8, height 5) with the 8 × 5 rectangle. Explain the relationship.
Find the trapezoid’s area by hand with A = ½(a + b)h.
For the circle with radius 5, find the area and circumference by hand (use π ≈ 3.14159). What happens to each if the radius doubles to 10?
Explain how the composite calculator found the area of the L-shape.
Show the working for the rectangle with a semicircle on one end.
Free from Geometry Lab · geometrylab.net · 6.G.A.1: Find the area of triangles, special quadrilaterals and polygons by composing them into rectangles or decomposing them into triangles and other shapes. 7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems. 7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.