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The area of a triangle is 36 cm2 and its height is 9 cm. Calculate the length of its base. Also, calculate the height of a triangle with an area of 180 cm2 and a base of 20 cm. Finally, calculate the

Mathematics

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Step-by-step solution

6 steps

The formula for the area of a triangle is given by:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

1)

  1. Identify the given values.

    Area =36 cm2= 36 \text{ cm}^2
    Height =9 cm= 9 \text{ cm}

  2. Substitute the values into the area formula and solve for the base.

    36=12×base×936 = \frac{1}{2} \times \text{base} \times 9 36=92×base36 = \frac{9}{2} \times \text{base}

    To find the base, multiply both sides by 29\frac{2}{9}:

    base=36×29\text{base} = 36 \times \frac{2}{9} base=729\text{base} = \frac{72}{9} base=8 cm\text{base} = 8 \text{ cm}

    The base of the triangle is 8 cm\boxed{\text{8 cm}}.

    2)

  3. Identify the given values.

    Area =180 cm2= 180 \text{ cm}^2
    Base =20 cm= 20 \text{ cm}

  4. Substitute the values into the area formula and solve for the height.

    180=12×20×height180 = \frac{1}{2} \times 20 \times \text{height} 180=10×height180 = 10 \times \text{height}

    To find the height, divide both sides by 10:

    height=18010\text{height} = \frac{180}{10} height=18 cm\text{height} = 18 \text{ cm}

    The height of the triangle is 18 cm\boxed{\text{18 cm}}.

    3)

  5. Identify the given values.

    Area =67.2 cm2= 67.2 \text{ cm}^2
    Height =16 cm= 16 \text{ cm}

  6. Substitute the values into the area formula and solve for the base.

    67.2=12×base×1667.2 = \frac{1}{2} \times \text{base} \times 16 67.2=8×base67.2 = 8 \times \text{base}

    To find the base, divide both sides by 8:

    base=67.28\text{base} = \frac{67.2}{8} base=8.4 cm\text{base} = 8.4 \text{ cm}

    The base of the triangle is 8.4 cm\boxed{\text{8.4 cm}}.

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