Calculate Areas of Composite Shapes - Grade 6

Grade 6 examples and questions on calculating areas of composite shapes and figures with detailed solutions and explanations are presented.

You first need to review the formulas to calculate areas for basic figures such as squares, rectangles, triangles, parallelograms and trapezoids.

Answer the Following Questions

Use the grid to determine the dimensions needed to and find the areas of the shapes shown below.

area of composite shapes .

Solutions to the Above Problems

Solution

The main idea is to decompose the given shape into known basic shapes such squares, rectangles, triangles, parallelogram and trapezoids and then use addition and/or subtraction to calculate the area of the given shape.

  1. The shape in part a) is shown below with the large rectangle completed.

    area of composite shape - question a).


    The area A of the given shape is calculated using 3 steps:

    1) calculate the area of the large rectangle ABWF : A1 = Length × Width = 5 × 3 = 15 unit 2

    2) Calculate the area of the small rectangle CWED : A2 = CW × WE = 3 × 1 = 3 unit 2

    3) Subtract the area of the small rectangle from that of the large rectangle: A = A1 - A2 = 15 - 3 = 12 unit 2


  2. The shape in part b) is shown below with the large rectangle completed.

    area of composite shape - question b).


    The area A of the given shape is calculated using 3 steps:

    1) calculate the area of the large rectangle GHZL : A1 = Length × Width = 5 × 3 = 15 unit 2

    2) Calculate the area of the trapezoid JIZK : A2 = (1/2) × ZK × (IZ + JK) = (1/2) × 1 ×(2 + 3)
    = (1/2) × 1 × 5 = (1/2) 5 = 5 / 2 = 2.5 unit 2

    3) Subtract the area of the trapezoid from that of the large rectangle: A = A1 - A2 = 15 - 2.5 = 12.5 unit 2


  3. The shape in part c) is shown below with the large rectangle completed.

    area of composite shape - question c).


    The area A of the given shape is calculated using 3 steps:

    1) calculate the area of the large rectangle QMNP : A1 = Length × Width = 5 × 3 = 15 unit 2

    2) Calculate the area of the triangle NOP : A2 = (1/2) × H × NP = (1/2) × 2 ×3 = (1/2) × 6 = 3 unit 2

    3) Subtract the area of the triangle from that of the large rectangle: A = A1 - A2 = 15 - 3 = 12 unit 2


  4. The shape in part d) is shown below with the large rectangle completed.

    area of composite shape - question d).


    The area A of the given shape is calculated using 4 steps:

    1) calculate the area of the large rectangle RA1BS : A1 = Length × Width = 5 × 3 = 15 unit 2

    2) Calculate the area of the triangle RA1V : A2 = (1/2) × RA1 × A1V = (1/2) × 3 ×2 = (1/2) × 5 = 2.5 unit 2

    3) Calculate the area of the triangle UBT : A3 = (1/2) × UB× BT = (1/2) × 1 ×1 = (1/2) = 0.5 unit 2

    3) Subtract the areas of the two triangles from that of the large rectangle: A = A1 - A2 - A3 = 15 - 2.5 - 0.5 = 12 unit 2

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