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What is the total area of the composite shape shown?

Mathematics

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Answer

72 cm2\text{72 cm}^2

Step-by-step solution

5 steps

  1. Divide the shape into three rectangles.

    The shape can be divided into a left vertical rectangle, a right vertical rectangle, and a middle horizontal rectangle.

  2. Calculate the area of the left vertical rectangle.

    The width of the left rectangle is 2 cm2 \text{ cm} and its height is 8 cm8 \text{ cm}.

    Arealeft=2 cm×8 cm=16 cm2\text{Area}_{\text{left}} = 2 \text{ cm} \times 8 \text{ cm} = 16 \text{ cm}^2

  3. Calculate the area of the right vertical rectangle.

    The width of the right rectangle is 5 cm5 \text{ cm} and its height is 8 cm8 \text{ cm}.

    Arearight=5 cm×8 cm=40 cm2\text{Area}_{\text{right}} = 5 \text{ cm} \times 8 \text{ cm} = 40 \text{ cm}^2

  4. Calculate the area of the middle horizontal rectangle.

    The length of the middle rectangle is 8 cm8 \text{ cm}. The total height of the shape is 8 cm8 \text{ cm}. The labels "3 cm" indicate the height of the cut-outs from the top and bottom. Therefore, the height of the middle rectangle is 8 cm−3 cm−3 cm=2 cm8 \text{ cm} - 3 \text{ cm} - 3 \text{ cm} = 2 \text{ cm}.

    Areamiddle=8 cm×2 cm=16 cm2\text{Area}_{\text{middle}} = 8 \text{ cm} \times 2 \text{ cm} = 16 \text{ cm}^2

  5. Sum the areas of the three rectangles to find the total area.

    Total Area=Arealeft+Arearight+Areamiddle\text{Total Area} = \text{Area}_{\text{left}} + \text{Area}_{\text{right}} + \text{Area}_{\text{middle}} Total Area=16 cm2+40 cm2+16 cm2=72 cm2\text{Total Area} = 16 \text{ cm}^2 + 40 \text{ cm}^2 + 16 \text{ cm}^2 = 72 \text{ cm}^2

    The total area of the shape is 72 cm2\text{72 cm}^2.

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