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7th grade · Math · Unit 20 of 20

Area of Composite Shapes

Split it, find each area, add

What your child practices

Finding the area of floors, walls, signs and gardens made of rectangles, triangles and trapezoids by splitting them into parts, adding the areas, or subtracting a cut-out part.

New York State Learning Standards learning standard: NY-7.G.6 · solving real-world problems with the area of shapes made of rectangles, triangles and trapezoids

How we explain it

Children can open this short lesson before they practice.

  1. Split the shape into rectangles, triangles and trapezoids.
  2. Rectangle: length × width. Triangle: ½ × base × height. Trapezoid: ½ × (sum of parallel sides) × height.
  3. Add the parts, or subtract a part that is cut out.

Example: A wall is a 10 ft by 8 ft rectangle with a triangle on top, base 10 ft and height 4 ft. What is its area? Rectangle: 10 × 8 = 80 ft². Triangle: ½ × 10 × 4 = 20 ft². 80 + 20 = 100. Answer: 100 ft²

Area of Composite Shapes in New York

In the New York State Learning Standards, this is unit 20 of 20 in 7th grade Math, after Slicing Solids.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Ana's patio is an L shape: a 8 ft by 5 ft rectangle joined to a 2 ft by 4 ft rectangle. What is its area, in square feet?

    • 38
    • 48
    • 40
    • 90

  2. Question 2

    A wall is a 12 ft by 8 ft rectangle with a triangle on top. The triangle's base is 12 ft and its height is 4 ft. What is the wall's area, in square feet?

    • 144
    • 123
    • 120
    • 96

  3. Question 3

    A floor is a 5 m by 5 m rectangle plus a 5 m by 5 m rectangle. Tile costs $4 per square meter. What does the tile cost, in dollars?

    • 50
    • 200
    • 100
    • 160

  4. Question 4

    A garden bed is a trapezoid with parallel sides of 10 m and 20 m, 7 m apart. What is its area, in m²?

    • 105
    • 70
    • 140
    • 210

  5. Question 5

    A 9 in by 10 in sign has a triangle cut out of one edge. The triangle's base is 6 in and its height is 4 in. What area is left, in square inches?

    • 102
    • 66
    • 78
    • 90

  6. Question 6

    Why is a triangle's area ½ × base × height?

    • it has 3 sides
    • it is half of a rectangle with the same base and height
    • it is half of a circle
    • the height is always half the base

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