Area of a Parallelogram Worksheet | Teach Starter - Free Printable

Problem Overview:

The task involves calculating the area of parallelograms and solving related word problems. The formula for the area of a parallelogram is:

\[
\text{Area} (A) = \text{Base} (B) \times \text{Height} (H)
\]

We will solve each part step by step.

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Part 1: Area of a Parallelogram

#### Question 1
- Base (B): 23 cm
- Height (H): 14 cm

\[
A = B \times H = 23 \, \text{cm} \times 14 \, \text{cm} = 322 \, \text{cm}^2
\]

#### Question 2
- Base (B): 12 cm
- Height (H): 6 cm

\[
A = B \times H = 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2
\]

#### Question 3
- Base (B): 57 mm
- Height (H): 29 mm

\[
A = B \times H = 57 \, \text{mm} \times 29 \, \text{mm} = 1653 \, \text{mm}^2
\]

#### Question 4
- Base (B): 17 km
- Height (H): 28 km

\[
A = B \times H = 17 \, \text{km} \times 28 \, \text{km} = 476 \, \text{km}^2
\]

#### Question 5
- Base (B): 30 mm
- Height (H): 5 mm

\[
A = B \times H = 30 \, \text{mm} \times 5 \, \text{mm} = 150 \, \text{mm}^2
\]

#### Question 6
- Base (B): 56 m
- Height (H): 12 m

\[
A = B \times H = 56 \, \text{m} \times 12 \, \text{m} = 672 \, \text{m}^2
\]

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Part 2: Using the Given Area to Find the Missing Value

#### Question 7
- Area: 725 mm²
- Base (B): 25 mm
- Height (H): ?

Using the formula \( A = B \times H \):

\[
725 \, \text{mm}^2 = 25 \, \text{mm} \times H
\]

Solve for \( H \):

\[
H = \frac{725 \, \text{mm}^2}{25 \, \text{mm}} = 29 \, \text{mm}
\]

#### Question 8
- Area: 85 cm²
- Height (H): 17 cm
- Base (B): ?

Using the formula \( A = B \times H \):

\[
85 \, \text{cm}^2 = B \times 17 \, \text{cm}
\]

Solve for \( B \):

\[
B = \frac{85 \, \text{cm}^2}{17 \, \text{cm}} = 5 \, \text{cm}
\]

#### Question 9
- Area: 480 km²
- Height (H): 32 km
- Base (B): ?

Using the formula \( A = B \times H \):

\[
480 \, \text{km}^2 = B \times 32 \, \text{km}
\]

Solve for \( B \):

\[
B = \frac{480 \, \text{km}^2}{32 \, \text{km}} = 15 \, \text{km}
\]

#### Question 10
- Area: 1,364 cm²
- Base (B): 44 cm
- Height (H): ?

Using the formula \( A = B \times H \):

\[
1,364 \, \text{cm}^2 = 44 \, \text{cm} \times H
\]

Solve for \( H \):

\[
H = \frac{1,364 \, \text{cm}^2}{44 \, \text{cm}} = 31 \, \text{cm}
\]

---

Part 3: Word Problems

#### Question 11
- Base (B): 48 cm
- Height (H): 12 cm

Calculate the area:

\[
A = B \times H = 48 \, \text{cm} \times 12 \, \text{cm} = 576 \, \text{cm}^2
\]

#### Question 12
- Area: 519 cm²
- Base (B): 29 cm
- Height (H): ?

Using the formula \( A = B \times H \):

\[
519 \, \text{cm}^2 = 29 \, \text{cm} \times H
\]

Solve for \( H \):

\[
H = \frac{519 \, \text{cm}^2}{29 \, \text{cm}} = 17.9 \, \text{cm}
\]

#### Question 13
- Parking Space Dimensions: 4 m long, 3 m wide
- Car Area: 10 m²

First, calculate the area of the parking space:

\[
A_{\text{parking}} = \text{Length} \times \text{Width} = 4 \, \text{m} \times 3 \, \text{m} = 12 \, \text{m}^2
\]

Compare the car's area (10 m²) with the parking space area (12 m²):

Since \( 10 \, \text{m}^2 < 12 \, \text{m}^2 \), the car will fit in the parking space.

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Final Answers:

1. \( 322 \, \text{cm}^2 \)
2. \( 72 \, \text{cm}^2 \)
3. \( 1653 \, \text{mm}^2 \)
4. \( 476 \, \text{km}^2 \)
5. \( 150 \, \text{mm}^2 \)
6. \( 672 \, \text{m}^2 \)

7. \( 29 \, \text{mm} \)
8. \( 5 \, \text{cm} \)
9. \( 15 \, \text{km} \)
10. \( 31 \, \text{cm} \)

11. \( 576 \, \text{cm}^2 \)
12. \( 17.9 \, \text{cm} \)
13. Yes, the car will fit.

\boxed{322, 72, 1653, 476, 150, 672, 29, 5, 15, 31, 576, 17.9, \text{Yes}}