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ABC is a triangle. Find the area of the shaded part.

Mathematics

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5 parts
11

12 cm2\text{12 cm}^2

12
4000 + 700 + 30 + 4
13
24
15
1700
16

9 tomato icons\text{9 tomato icons}

Step-by-step solution

10 steps

Here are the solutions to the problems:

Part 11· 3 steps

To find the area of the shaded part, we identify it as a triangle.

  1. Identify the base and height of the shaded triangle.

    The height of the shaded triangle is given as 4 cm4 \text{ cm}.
    The base of the shaded triangle is given as 6 cm6 \text{ cm}.

  2. Use the formula for the area of a triangle.

    The area of a triangle is given by the formula:

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  3. Substitute the values and calculate the area.

    Area=12×6 cm×4 cm\text{Area} = \frac{1}{2} \times 6 \text{ cm} \times 4 \text{ cm} Area=12×24 cm2\text{Area} = \frac{1}{2} \times 24 \text{ cm}^2 Area=12 cm2\text{Area} = 12 \text{ cm}^2

    The area of the shaded part is 12 cm2\boxed{\text{12 cm}^2}.

Part 124000 + 700 + 30 + 4

To expand 4734, we write it in terms of its place values.

  1. Identify the place value of each digit.

    The digit 4 is in the thousands place (4×10004 \times 1000).
    The digit 7 is in the hundreds place (7×1007 \times 100).
    The digit 3 is in the tens place (3×103 \times 10).
    The digit 4 is in the ones place (4×14 \times 1).

  2. Write the number as the sum of its place values.

    4734=4000+700+30+44734 = 4000 + 700 + 30 + 4

    The expanded form of 4734 is 4000+700+30+4\boxed{4000 + 700 + 30 + 4}.

Part 1324

To find the least number of mangoes that can be shared among 6 and 8 pupils with no remainder, we need to find the Least Common Multiple (LCM) of 6 and 8.

  1. List the multiples of each number.

    Multiples of 6: 6,12,18,24,30,…6, 12, 18, \textbf{24}, 30, \dots
    Multiples of 8: 8,16,24,32,…8, 16, \textbf{24}, 32, \dots

  2. Identify the smallest common multiple.

    The least common multiple of 6 and 8 is 24.
    The least number of mangoes is 24\boxed{24}.

Part 151700

To round off 1678 to the nearest hundreds, we look at the tens digit.

  1. Identify the hundreds digit and the digit to its right.

    The hundreds digit is 6.
    The digit to its right (the tens digit) is 7.

  2. Apply the rounding rule.

    Since the tens digit (7) is 5 or greater, we round up the hundreds digit.
    The hundreds digit 6 becomes 7. All digits to the right of the hundreds place become 0.

    1678≈17001678 \approx 1700

    1678 rounded to the nearest hundreds is 1700\boxed{1700}.

Part 16

9 tomato icons\text{9 tomato icons}

Given that one tomato icon represents 10 tomatoes, we need to represent 90 tomatoes.

  1. Determine how many icons are needed.

    Divide the total number of tomatoes by the value of one icon:

    Number of icons=Total tomatoesTomatoes per icon\text{Number of icons} = \frac{\text{Total tomatoes}}{\text{Tomatoes per icon}} Number of icons=9010=9\text{Number of icons} = \frac{90}{10} = 9

    To represent 90 tomatoes, you would draw 9 tomato icons\boxed{\text{9 tomato icons}}.

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