To solve the problem of finding the areas of the given shapes, we will calculate each shape's area step by step using the appropriate formulas. Let's go through each shape one by one.
---
1. Triangle
Given:
- Base = 4 cm
- Height = 3 cm
Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm} = \frac{1}{2} \times 12 \, \text{cm}^2 = 6 \, \text{cm}^2
\]
Answer for the triangle:
\[
\boxed{6 \, \text{cm}^2}
\]
---
2. Rectangle
Given:
- Length = 2 cm
- Width = 3 cm
Formula for the area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]
Calculation:
\[
\text{Area} = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2
\]
Answer for the rectangle:
\[
\boxed{6 \, \text{cm}^2}
\]
---
3. Square
Given:
- Side length = 5 cm
Formula for the area of a square:
\[
\text{Area} = \text{side}^2
\]
Calculation:
\[
\text{Area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]
Answer for the square:
\[
\boxed{25 \, \text{cm}^2}
\]
---
4. Parallelogram
Given:
- Base = 7 cm
- Height = 3 cm
Formula for the area of a parallelogram:
\[
\text{Area} = \text{base} \times \text{height}
\]
Calculation:
\[
\text{Area} = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]
Answer for the parallelogram:
\[
\boxed{21 \, \text{cm}^2}
\]
---
5. Trapezoid
Given:
- Top base (\(b_1\)) = 4 cm
- Bottom base (\(b_2\)) = 8 cm
- Height = 3 cm
Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (\text{top base} + \text{bottom base}) \times \text{height}
\]
Calculation:
\[
\text{Area} = \frac{1}{2} \times (4 \, \text{cm} + 8 \, \text{cm}) \times 3 \, \text{cm} = \frac{1}{2} \times 12 \, \text{cm} \times 3 \, \text{cm} = \frac{1}{2} \times 36 \, \text{cm}^2 = 18 \, \text{cm}^2
\]
Answer for the trapezoid:
\[
\boxed{18 \, \text{cm}^2}
\]
---
6. Circle
Given:
- Diameter = 10 cm
- Radius (\(r\)) = \(\frac{\text{diameter}}{2} = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm}\)
Formula for the area of a circle:
\[
\text{Area} = \pi \times r^2
\]
Calculation:
\[
\text{Area} = \pi \times (5 \, \text{cm})^2 = \pi \times 25 \, \text{cm}^2 = 25\pi \, \text{cm}^2
\]
Using \(\pi \approx 3.14\):
\[
\text{Area} \approx 25 \times 3.14 = 78.5 \, \text{cm}^2
\]
Answer for the circle:
\[
\boxed{78.5 \, \text{cm}^2}
\]
---
Final Answers:
1. Triangle: \(\boxed{6 \, \text{cm}^2}\)
2. Rectangle: \(\boxed{6 \, \text{cm}^2}\)
3. Square: \(\boxed{25 \, \text{cm}^2}\)
4. Parallelogram: \(\boxed{21 \, \text{cm}^2}\)
5. Trapezoid: \(\boxed{18 \, \text{cm}^2}\)
6. Circle: \(\boxed{78.5 \, \text{cm}^2}\)
Parent Tip: Review the logic above to help your child master the concept of 6th grade geometry worksheet pdf.
