Math 6 homework worksheet featuring six word problems on area and perimeter, including calculating land area, fertilizer needed, fabric for a triangular piece, jogging distance, fencing for a garden, and brownie area.

Problem Set: Area and Perimeter Word Problems

Below, I will solve each problem step by step, showing all work and including proper units of measure.

---

#### Problem 1:
Norman is a sunflower farmer. He uses a plot of land that is 3 km by 4.3 km. How much land does he use for his sunflowers?

- Step 1: Identify the shape and formula.
The plot of land is rectangular, so we use the formula for the area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]

- Step 2: Substitute the given values.
\[
\text{Length} = 3 \, \text{km}, \quad \text{Width} = 4.3 \, \text{km}
\]
\[
\text{Area} = 3 \, \text{km} \times 4.3 \, \text{km}
\]

- Step 3: Perform the multiplication.
\[
3 \times 4.3 = 12.9
\]

- Step 4: Include the units.
\[
\text{Area} = 12.9 \, \text{km}^2
\]

- Final Answer:
\[
\boxed{12.9 \, \text{km}^2}
\]

---

#### Problem 2:
Joanna created a triangular-shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 1.4 m and a height of 2.6 m, how much fertilizer will she need?

- Step 1: Identify the shape and formula.
The garden is triangular, so we use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

- Step 2: Substitute the given values.
\[
\text{Base} = 1.4 \, \text{m}, \quad \text{Height} = 2.6 \, \text{m}
\]
\[
\text{Area} = \frac{1}{2} \times 1.4 \, \text{m} \times 2.6 \, \text{m}
\]

- Step 3: Perform the multiplication.
\[
1.4 \times 2.6 = 3.64
\]
\[
\frac{1}{2} \times 3.64 = 1.82
\]

- Step 4: Include the units.
\[
\text{Area} = 1.82 \, \text{m}^2
\]

- Final Answer:
\[
\boxed{1.82 \, \text{m}^2}
\]

---

#### Problem 3:
Sue bought a triangular-shaped piece of wood with a height of 6 inches and a base of 2 inches. She plans to cover the front with a piece of fabric. How much fabric will she need?

- Step 1: Identify the shape and formula.
The piece of wood is triangular, so we use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

- Step 2: Substitute the given values.
\[
\text{Base} = 2 \, \text{inches}, \quad \text{Height} = 6 \, \text{inches}
\]
\[
\text{Area} = \frac{1}{2} \times 2 \, \text{inches} \times 6 \, \text{inches}
\]

- Step 3: Perform the multiplication.
\[
2 \times 6 = 12
\]
\[
\frac{1}{2} \times 12 = 6
\]

- Step 4: Include the units.
\[
\text{Area} = 6 \, \text{square inches}
\]

- Final Answer:
\[
\boxed{6 \, \text{square inches}}
\]

---

#### Problem 4:
Before soccer practice, Allyson jogs around the field that measures 100 yards by 65 yards twice. How far will she jog?

- Step 1: Identify the shape and formula.
The field is rectangular, so we use the formula for the perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]

- Step 2: Substitute the given values.
\[
\text{Length} = 100 \, \text{yards}, \quad \text{Width} = 65 \, \text{yards}
\]
\[
\text{Perimeter} = 2 \times (100 \, \text{yards} + 65 \, \text{yards})
\]

- Step 3: Perform the addition inside the parentheses.
\[
100 + 65 = 165
\]
\[
\text{Perimeter} = 2 \times 165 = 330 \, \text{yards}
\]

- Step 4: Since Allyson jogs around the field twice, multiply the perimeter by 2.
\[
\text{Total distance} = 330 \, \text{yards} \times 2 = 660 \, \text{yards}
\]

- Final Answer:
\[
\boxed{660 \, \text{yards}}
\]

---

#### Problem 5:
A farmer needs to buy fencing to go around his garden. The garden is 200 feet long by 150 feet wide. How much fencing will he need?

- Step 1: Identify the shape and formula.
The garden is rectangular, so we use the formula for the perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]

- Step 2: Substitute the given values.
\[
\text{Length} = 200 \, \text{feet}, \quad \text{Width} = 150 \, \text{feet}
\]
\[
\text{Perimeter} = 2 \times (200 \, \text{feet} + 150 \, \text{feet})
\]

- Step 3: Perform the addition inside the parentheses.
\[
200 + 150 = 350
\]
\[
\text{Perimeter} = 2 \times 350 = 700 \, \text{feet}
\]

- Final Answer:
\[
\boxed{700 \, \text{feet}}
\]

---

#### Problem 6:
Joel has brownies. The length of each brownie is 7 cm and the width is 5 cm. Find the area of the brownies.

- Step 1: Identify the shape and formula.
Each brownie is rectangular, so we use the formula for the area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]

- Step 2: Substitute the given values.
\[
\text{Length} = 7 \, \text{cm}, \quad \text{Width} = 5 \, \text{cm}
\]
\[
\text{Area} = 7 \, \text{cm} \times 5 \, \text{cm}
\]

- Step 3: Perform the multiplication.
\[
7 \times 5 = 35
\]

- Step 4: Include the units.
\[
\text{Area} = 35 \, \text{cm}^2
\]

- Final Answer:
\[
\boxed{35 \, \text{cm}^2}
\]

---

Final Answers:

1. \(\boxed{12.9 \, \text{km}^2}\)
2. \(\boxed{1.82 \, \text{m}^2}\)
3. \(\boxed{6 \, \text{square inches}}\)
4. \(\boxed{660 \, \text{yards}}\)
5. \(\boxed{700 \, \text{feet}}\)
6. \(\boxed{35 \, \text{cm}^2}\)