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Provide properties of a parallelogram, rhombus, and trapezoid, and solve problems involving the area of a square and probability.

Mathematics

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1. Give 3 properties of the following shapes:

Part a

Parallelogram

  • Opposite sides are parallel.
  • Opposite sides are equal in length.
  • Opposite angles are equal.

Part b

Rhombus

  • All four sides are equal in length.
  • Opposite angles are equal.
  • Diagonals bisect each other at right angles.

Part c· 16 steps

Trapezoid

  • It has at least one pair of parallel sides.
  • The sum of angles between parallel sides is 180∘180^\circ.
  • The non-parallel sides are called legs.

2. Find the area of a square with length 9cm.

  1. Recall the formula for the area of a square.

    The area of a square is given by A=s2A = s^2, where ss is the side length.

  2. Substitute the given side length into the formula.

    A=(9 cm)2A = (9 \text{ cm})^2
  3. Calculate the area.

    A=81 cm2A = 81 \text{ cm}^2

    The area of the square is 81 cm2\boxed{\text{81 cm}^2}.

    3. What is the probability of picking a red ball from a bag with 3 red balls and 2 blue balls.

  4. Determine the total number of balls and the number of red balls.

    Number of red balls = 3
    Number of blue balls = 2
    Total number of balls = 3+2=53 + 2 = 5

  5. Calculate the probability.

    Probability of picking a red ball = Number of red ballsTotal number of balls\frac{\text{Number of red balls}}{\text{Total number of balls}}

    P(red ball)=35P(\text{red ball}) = \frac{3}{5}

    The probability of picking a red ball is 35\boxed{\frac{3}{5}}.

    4. A coin is flipped. What is the chance it lands on heads.

  6. Identify the possible outcomes when flipping a coin.

    The possible outcomes are Heads (H) or Tails (T). There are 2 possible outcomes.

  7. Determine the number of favorable outcomes for landing on heads.

    There is 1 favorable outcome (Heads).

  8. Calculate the probability.

    Probability of landing on heads = Number of favorable outcomesTotal number of outcomes\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

    P(heads)=12P(\text{heads}) = \frac{1}{2}

    The chance of landing on heads is 12\boxed{\frac{1}{2}}.

    5. What is the place value of 7 in 3,745.

  9. Identify the digits in the number 3,745.

    The digits are 3 (thousands place), 7 (hundreds place), 4 (tens place), and 5 (ones place).

  10. Determine the place value of the digit 7.

    The digit 7 is in the hundreds place.
    The place value of 7 is 7×100=7007 \times 100 = 700.
    The place value of 7 in 3,745 is Hundreds (or 700)\boxed{\text{Hundreds (or 700)}}.

    6. Find the perimeter of a rectangle with length 8cm and width 5cm.

  11. Recall the formula for the perimeter of a rectangle.

    The perimeter of a rectangle is given by P=2(l+w)P = 2(l + w), where ll is the length and ww is the width.

  12. Substitute the given length and width into the formula.

    P=2(8 cm+5 cm)P = 2(8 \text{ cm} + 5 \text{ cm})
  13. Calculate the perimeter.

    P=2(13 cm)P = 2(13 \text{ cm}) P=26 cmP = 26 \text{ cm}

    The perimeter of the rectangle is 26 cm\boxed{\text{26 cm}}.

    7. Convert 3.7kg to grams.

  14. Recall the conversion factor between kilograms and grams.

    1 kg=1000 g1 \text{ kg} = 1000 \text{ g}

  15. Multiply the given mass in kilograms by the conversion factor.

    3.7 kg×1000 g1 kg3.7 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}}
  16. Perform the multiplication.

    3.7×1000 g=3700 g3.7 \times 1000 \text{ g} = 3700 \text{ g}

    3.7 kg3.7 \text{ kg} is equal to 3700 g\boxed{\text{3700 g}}.

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