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Give the formula for the area of the following figures: a square, a rectangular, a triangular

Mathematics

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  1. Give the formula for the area of the following figures.

    • 1.1.1 A square: The formula for the area of a square is the side length squared. Area=side×side=s2\text{Area} = \text{side} \times \text{side} = s^2
    • 1.1.2 A rectangular: The formula for the area of a rectangle is length multiplied by width. Area=length×width=l×w\text{Area} = \text{length} \times \text{width} = l \times w
    • 1.1.3 A triangular: The formula for the area of a triangle is half of the base multiplied by the height. Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  2. Determine the area of the square ABCD with AB = 3 cm.

    The side length of the square is s=3 cms = 3 \text{ cm}.

    Area=s2\text{Area} = s^2 Area=(3 cm)2\text{Area} = (3 \text{ cm})^2 Area=9 cm2\text{Area} = 9 \text{ cm}^2

    The area of the square ABCD is 9 cm2\boxed{\text{9 cm}^2}.

  3. Determine the area of the rectangular ABCD with AB = 5 cm and BC = 3 cm.

    The length of the rectangle is l=5 cml = 5 \text{ cm} and the width is w=3 cmw = 3 \text{ cm}.

    Area=l×w\text{Area} = l \times w Area=5 cm×3 cm\text{Area} = 5 \text{ cm} \times 3 \text{ cm} Area=15 cm2\text{Area} = 15 \text{ cm}^2

    The area of the rectangular ABCD is 15 cm2\boxed{\text{15 cm}^2}.

  4. Determine the area of the triangular ABC with AC = 5 cm and height DB = 30 mm.

    First, convert the height from millimeters to centimeters:

    30 mm=3 cm30 \text{ mm} = 3 \text{ cm}

    The base of the triangle is AC=5 cm\text{AC} = 5 \text{ cm} and the height is DB=3 cm\text{DB} = 3 \text{ cm}.

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} Area=12×5 cm×3 cm\text{Area} = \frac{1}{2} \times 5 \text{ cm} \times 3 \text{ cm} Area=12×15 cm2\text{Area} = \frac{1}{2} \times 15 \text{ cm}^2 Area=7.5 cm2\text{Area} = 7.5 \text{ cm}^2

    The area of the triangular ABC is 7.5 cm2\boxed{\text{7.5 cm}^2}.

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