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Calculate the area of a composite shape made of a rectangle and a triangle, and its perimeter.

Mathematics

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4 parts
a

60 m2\text{60 m}^2

b

20 m2\text{20 m}^2

c

80 m2\text{80 m}^2

d

34.80 m\text{34.80 m}

Step-by-step solution

7 steps

Part a· 2 steps

  1. Identify the dimensions of the rectangular part.

    The width of the rectangle is 10 m and the height is 6 m.

  2. Calculate the area of the rectangular part.

    Arearectangle=width×height\text{Area}_{\text{rectangle}} = \text{width} \times \text{height} Arearectangle=10 m×6 m\text{Area}_{\text{rectangle}} = 10 \text{ m} \times 6 \text{ m} Arearectangle=60 m2\text{Area}_{\text{rectangle}} = 60 \text{ m}^2

    The area of the rectangular part is 60 m2\boxed{\text{60 m}^2}.

Part b

20 m2\text{20 m}^2

  1. Identify the dimensions of the triangular part.

    The base of the triangle is 10 m and the perpendicular height is 4 m.

  2. Calculate the area of the triangular part.

    Areatriangle=12×base×perpendicular height\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{perpendicular height} Areatriangle=12×10 m×4 m\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \text{ m} \times 4 \text{ m} Areatriangle=5 m×4 m\text{Area}_{\text{triangle}} = 5 \text{ m} \times 4 \text{ m} Areatriangle=20 m2\text{Area}_{\text{triangle}} = 20 \text{ m}^2

    The area of the triangular part is 20 m2\boxed{\text{20 m}^2}.

Part c

80 m2\text{80 m}^2

  1. Add the areas of the rectangular and triangular parts.

    Total Area=Arearectangle+Areatriangle\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} Total Area=60 m2+20 m2\text{Total Area} = 60 \text{ m}^2 + 20 \text{ m}^2 Total Area=80 m2\text{Total Area} = 80 \text{ m}^2

    The total area of the composite shape is 80 m2\boxed{\text{80 m}^2}.

Part d

34.80 m\text{34.80 m}

  1. Identify all the external sides that form the perimeter.

    The perimeter consists of the base of the rectangle (10 m), the two vertical sides of the rectangle (6 m each), and the two slant sides of the triangle (6.40 m each).

  2. Calculate the total perimeter.

    Perimeter=rectangle base+2×rectangle height+2×triangle slant side\text{Perimeter} = \text{rectangle base} + 2 \times \text{rectangle height} + 2 \times \text{triangle slant side} Perimeter=10 m+(2×6 m)+(2×6.40 m)\text{Perimeter} = 10 \text{ m} + (2 \times 6 \text{ m}) + (2 \times 6.40 \text{ m}) Perimeter=10 m+12 m+12.80 m\text{Perimeter} = 10 \text{ m} + 12 \text{ m} + 12.80 \text{ m} Perimeter=34.80 m\text{Perimeter} = 34.80 \text{ m}

    The perimeter of the shape is 34.80 m\boxed{\text{34.80 m}}.

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