Gorgeous Gardens

Solution

They will plant 845 plants in all.

Explanation

figure
All the angles are right angles.
figure
All 4 sides are equal and all angles are right angles.

figure
figure
figure

To solve, follow these steps:

First, use the clues to find out who owns which garden.

  1. Clue: Raymon's garden has more right angles than Kate's garden, but Augustin's garden has the most right angles of all. Although the square and the inside of the parallelogram have right angles, the figure has the most right angles of all. Therefore, the figure garden belongs to Augustin, the square garden is Raymon's, and the parallelogram is Kate's.
  2. The 3rd clue is the most helpful clue to consider next: Not all the sides of Lillian's garden are straight. The radius of the round part of her garden is one-half the height of Cindy's garden. This means that Lillian has the garden with the curved top: figure
    The radius of that half circle is 3, which is half of 6. The height of the trapezoid is 6. This means that Cindy must have the trapezoid:
    figure
  3. The base of Kate's garden is 1 foot longer than the base of Cindy's garden. This confirms that Kate's garden is the parallelogram because its base is 8. Cindy has the trapezoid because its longest base is 7.

Second, find the number of square feet for each garden.

  1. Augustin's garden:
    Augustin's Garden

    1. The two rectangles have the same length. To find the length of one side, add: 1 + 3 + 1 = 5
    2. Find the area by separating the figure into simple figures. First, find the area of the middle square: The area of a square is bh or s x s. 5 x 5 = 25 ft²
    3. Find the area of the outside rectangles: 2 x 3 = 6 ft² for each.
    4. Add: 25 + 6 + 6 = 37 ft²

  2. Raymon's garden:
    figure

    1. Raymon's garden is the square. Each side is 6 ft. The area of a square is bh or s x s. Multiply: s x s
    2. 6 x 6 = 36 ft²

  3. Cindy's garden:
    figure

    1. Find the area of the center rectangle: A = bh
      3 x 6 = 18 ft²
    2. Find the area of each triangle: one-halfbh
      one-half (6)(2) = 6 ft² for each triangle.
    3. Add the area of both triangles and the rectangle: 18 ft² + 6 ft² + 6 ft² = 30 ft².

  4. Lillian's garden:
    figure

    1. Find the area by separating the figure into simple figures. To find the area of the half circle, find the area of a circle, then divide the area in half:
    2. A=π r²
      Area of the whole circle =3.14 x 3².
      = 3.14 x 9 = 28.26 ft². Area of the half circle = 14.13 ft.
    3. Find the area of the rectangle formed by the diameter and the 3 outside straight lines:
      figure
      A = bh.
      6 x 4 = 24 ft²
    4. Add 24 ft²+ 14.13 ft² = 38.13 ft².
    5. Round to 38 ft².

  5. Kate's garden:
    1. Kate's garden is a parallelogram. The area of a parallelogram is A = bh.
    2. The base is 8; the height is 4.
      A = 8 x 4
      A = 32 ft²

Third, find out how many plants will fit in each garden.

  1. Add the number of square feet in each garden to find out the total number of square feet in all the gardens together:

    Garden Square Feet
    Augustin's 37 ft²
    Raymon's 36 ft²
    Cindy's 30 ft²
    Lillian's 38 ft²
    Kate's 32 ft²
    Total Square Feet 173 ft²

  2. Multiply the number of total square feet by 5 because 5 plants fit in each square foot:
    173 x 5 = 865 plants in all
  3. They will plant 865 plants in all

    Another way to do the last part is like this:
    Multiply the number of square feet in each garden by 5 to find out how many plants fit in each garden. Then add the total number of plants in each garden together to find out how many plants in all:

    Garden Square feet Multiply by the number of plants per square foot Number of plants
    Augustin's 37 ft² x 5 = 185
    Raymon's 36 ft² x 5 = 180
    Cindy's 30 ft² x 5 = 150
    Lillian's 38 ft² x 5 = 190
    Kate's 32 ft² x 5 = 160
    Total 173 ft² 865


Houghton Mifflin Math Grade 6