Math worksheet for finding the area of different geometric shapes using appropriate formulas.
Worksheet titled "Finding Area" with 10 problems to calculate the area of various shapes including rectangles, squares, triangles, and trapezoids using given formulas and dimensions.
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Step-by-step solution for: Finding Different Shapes Area Worksheet | Area ...
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Show Answer Key & Explanations
Step-by-step solution for: Finding Different Shapes Area Worksheet | Area ...
To solve the problem of finding the area of each shape, we will use the provided formulas for different shapes:
1. Rectangle/Square: \( A = l \times w \)
2. Trapezoid: \( A = \frac{(a + b)}{2} \times h \)
3. Triangle: \( A = \frac{b \times h}{2} \)
4. Right Triangle: \( A = \frac{a \times b}{2} \)
Let's calculate the area for each shape step by step.
---
- Dimensions: \( l = 30 \, \text{m} \), \( w = 14 \, \text{m} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 30 \times 14 = 420 \, \text{m}^2 \)
- Answer: \( 420 \, \text{m}^2 \)
---
- Side length: \( s = 9 \, \text{ft} \)
- Formula: \( A = s \times s \)
- Calculation: \( A = 9 \times 9 = 81 \, \text{ft}^2 \)
- Answer: \( 81 \, \text{ft}^2 \)
---
- Dimensions: \( l = 27 \, \text{cm} \), \( w = 10 \, \text{cm} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 27 \times 10 = 270 \, \text{cm}^2 \)
- Answer: \( 270 \, \text{cm}^2 \)
---
- Base: \( b = 18 \, \text{in} \)
- Height: \( h = 12 \, \text{in} \)
- Formula: \( A = \frac{b \times h}{2} \)
- Calculation: \( A = \frac{18 \times 12}{2} = \frac{216}{2} = 108 \, \text{in}^2 \)
- Answer: \( 108 \, \text{in}^2 \)
---
- Bases: \( a = 8 \, \text{mm} \), \( b = 20 \, \text{mm} \)
- Height: \( h = 13 \, \text{mm} \)
- Formula: \( A = \frac{(a + b)}{2} \times h \)
- Calculation: \( A = \frac{(8 + 20)}{2} \times 13 = \frac{28}{2} \times 13 = 14 \times 13 = 182 \, \text{mm}^2 \)
- Answer: \( 182 \, \text{mm}^2 \)
---
- Legs: \( a = 11 \, \text{yd} \), \( b = 14 \, \text{yd} \)
- Formula: \( A = \frac{a \times b}{2} \)
- Calculation: \( A = \frac{11 \times 14}{2} = \frac{154}{2} = 77 \, \text{yd}^2 \)
- Answer: \( 77 \, \text{yd}^2 \)
---
- Dimensions: \( l = 48 \, \text{mi} \), \( w = 38 \, \text{mi} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 48 \times 38 = 1824 \, \text{mi}^2 \)
- Answer: \( 1824 \, \text{mi}^2 \)
---
- Bases: \( a = 50 \, \text{km} \), \( b = 140 \, \text{km} \)
- Height: \( h = 50 \, \text{km} \)
- Formula: \( A = \frac{(a + b)}{2} \times h \)
- Calculation: \( A = \frac{(50 + 140)}{2} \times 50 = \frac{190}{2} \times 50 = 95 \times 50 = 4750 \, \text{km}^2 \)
- Answer: \( 4750 \, \text{km}^2 \)
---
- Base: \( b = 120 \, \text{cm} \)
- Height: \( h = 95 \, \text{cm} \)
- Formula: \( A = \frac{b \times h}{2} \)
- Calculation: \( A = \frac{120 \times 95}{2} = \frac{11400}{2} = 5700 \, \text{cm}^2 \)
- Answer: \( 5700 \, \text{cm}^2 \)
---
- Dimensions: \( l = 221 \, \text{ft} \), \( w = 121 \, \text{ft} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 221 \times 121 = 26741 \, \text{ft}^2 \)
- Answer: \( 26741 \, \text{ft}^2 \)
---
1. \( 420 \, \text{m}^2 \)
2. \( 81 \, \text{ft}^2 \)
3. \( 270 \, \text{cm}^2 \)
4. \( 108 \, \text{in}^2 \)
5. \( 182 \, \text{mm}^2 \)
6. \( 77 \, \text{yd}^2 \)
7. \( 1824 \, \text{mi}^2 \)
8. \( 4750 \, \text{km}^2 \)
9. \( 5700 \, \text{cm}^2 \)
10. \( 26741 \, \text{ft}^2 \)
\[
\boxed{
\begin{array}{ll}
1. & 420 \, \text{m}^2 \\
2. & 81 \, \text{ft}^2 \\
3. & 270 \, \text{cm}^2 \\
4. & 108 \, \text{in}^2 \\
5. & 182 \, \text{mm}^2 \\
6. & 77 \, \text{yd}^2 \\
7. & 1824 \, \text{mi}^2 \\
8. & 4750 \, \text{km}^2 \\
9. & 5700 \, \text{cm}^2 \\
10. & 26741 \, \text{ft}^2 \\
\end{array}
}
\]
1. Rectangle/Square: \( A = l \times w \)
2. Trapezoid: \( A = \frac{(a + b)}{2} \times h \)
3. Triangle: \( A = \frac{b \times h}{2} \)
4. Right Triangle: \( A = \frac{a \times b}{2} \)
Let's calculate the area for each shape step by step.
---
1. Rectangle
- Dimensions: \( l = 30 \, \text{m} \), \( w = 14 \, \text{m} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 30 \times 14 = 420 \, \text{m}^2 \)
- Answer: \( 420 \, \text{m}^2 \)
---
2. Square
- Side length: \( s = 9 \, \text{ft} \)
- Formula: \( A = s \times s \)
- Calculation: \( A = 9 \times 9 = 81 \, \text{ft}^2 \)
- Answer: \( 81 \, \text{ft}^2 \)
---
3. Rectangle
- Dimensions: \( l = 27 \, \text{cm} \), \( w = 10 \, \text{cm} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 27 \times 10 = 270 \, \text{cm}^2 \)
- Answer: \( 270 \, \text{cm}^2 \)
---
4. Triangle
- Base: \( b = 18 \, \text{in} \)
- Height: \( h = 12 \, \text{in} \)
- Formula: \( A = \frac{b \times h}{2} \)
- Calculation: \( A = \frac{18 \times 12}{2} = \frac{216}{2} = 108 \, \text{in}^2 \)
- Answer: \( 108 \, \text{in}^2 \)
---
5. Trapezoid
- Bases: \( a = 8 \, \text{mm} \), \( b = 20 \, \text{mm} \)
- Height: \( h = 13 \, \text{mm} \)
- Formula: \( A = \frac{(a + b)}{2} \times h \)
- Calculation: \( A = \frac{(8 + 20)}{2} \times 13 = \frac{28}{2} \times 13 = 14 \times 13 = 182 \, \text{mm}^2 \)
- Answer: \( 182 \, \text{mm}^2 \)
---
6. Right Triangle
- Legs: \( a = 11 \, \text{yd} \), \( b = 14 \, \text{yd} \)
- Formula: \( A = \frac{a \times b}{2} \)
- Calculation: \( A = \frac{11 \times 14}{2} = \frac{154}{2} = 77 \, \text{yd}^2 \)
- Answer: \( 77 \, \text{yd}^2 \)
---
7. Rectangle
- Dimensions: \( l = 48 \, \text{mi} \), \( w = 38 \, \text{mi} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 48 \times 38 = 1824 \, \text{mi}^2 \)
- Answer: \( 1824 \, \text{mi}^2 \)
---
8. Trapezoid
- Bases: \( a = 50 \, \text{km} \), \( b = 140 \, \text{km} \)
- Height: \( h = 50 \, \text{km} \)
- Formula: \( A = \frac{(a + b)}{2} \times h \)
- Calculation: \( A = \frac{(50 + 140)}{2} \times 50 = \frac{190}{2} \times 50 = 95 \times 50 = 4750 \, \text{km}^2 \)
- Answer: \( 4750 \, \text{km}^2 \)
---
9. Triangle
- Base: \( b = 120 \, \text{cm} \)
- Height: \( h = 95 \, \text{cm} \)
- Formula: \( A = \frac{b \times h}{2} \)
- Calculation: \( A = \frac{120 \times 95}{2} = \frac{11400}{2} = 5700 \, \text{cm}^2 \)
- Answer: \( 5700 \, \text{cm}^2 \)
---
10. Rectangle
- Dimensions: \( l = 221 \, \text{ft} \), \( w = 121 \, \text{ft} \)
- Formula: \( A = l \times w \)
- Calculation: \( A = 221 \times 121 = 26741 \, \text{ft}^2 \)
- Answer: \( 26741 \, \text{ft}^2 \)
---
Final Answers
1. \( 420 \, \text{m}^2 \)
2. \( 81 \, \text{ft}^2 \)
3. \( 270 \, \text{cm}^2 \)
4. \( 108 \, \text{in}^2 \)
5. \( 182 \, \text{mm}^2 \)
6. \( 77 \, \text{yd}^2 \)
7. \( 1824 \, \text{mi}^2 \)
8. \( 4750 \, \text{km}^2 \)
9. \( 5700 \, \text{cm}^2 \)
10. \( 26741 \, \text{ft}^2 \)
\[
\boxed{
\begin{array}{ll}
1. & 420 \, \text{m}^2 \\
2. & 81 \, \text{ft}^2 \\
3. & 270 \, \text{cm}^2 \\
4. & 108 \, \text{in}^2 \\
5. & 182 \, \text{mm}^2 \\
6. & 77 \, \text{yd}^2 \\
7. & 1824 \, \text{mi}^2 \\
8. & 4750 \, \text{km}^2 \\
9. & 5700 \, \text{cm}^2 \\
10. & 26741 \, \text{ft}^2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of finding the area worksheet.
