Teacher Guide: Area of Parallelograms
Learn how to calculate the area of a parallelogram using the base and height formula.
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Class quiz
10 questions on Area & Perimeter. Students join with a name, you see everyone's score.
For Teachers
- Identify the base and height of a parallelogram
- Apply the formula to calculate area
- Distinguish between the height and slant side
- Solve real-world problems involving parallelogram areas
- Express area in appropriate square units
- • Understanding of multiplication
- • Knowledge of what perpendicular means
- • Familiarity with units of measurement
- • Basic understanding of quadrilaterals
- 1. Why do you think the area formula for a parallelogram is the same as for a rectangle?
- 2. If you double the height of a parallelogram, what happens to its area?
- 3. Can two parallelograms with different shapes have the same area? How?
- 4. Where have you seen parallelogram shapes in buildings or objects around you?
The height is always one of the sides of the parallelogram
Tilting a rectangle changes its area
For Struggling Students:
- • Start with rectangles and gradually tilt them into parallelograms
- • Use graph paper to count squares inside the parallelogram
- • Provide templates with height already drawn and labeled
For On-Level Students:
- • Find area when height is inside vs. outside the parallelogram
- • Solve for missing base or height given the area
- • Compare areas of parallelograms with same perimeter but different heights
For Advanced Students:
- • Explore how area changes when angles change but sides stay the same
- • Calculate area using trigonometry ()
- • Connect to vectors and the cross product
- 6.G.A.1 (CCSS.MATH.CONTENT.6.G.A.1)
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
- 6.G.A.3 (CCSS.MATH.CONTENT.6.G.A.3)
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side
- visualInteractive Parallelogram
Drag to change base and height, see area update in real-time
- activityRectangle to Parallelogram
See how a rectangle transforms into a parallelogram while keeping the same area
- worksheetFind the Missing Dimension
Given area and one dimension, find the other
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- is the base (any side of the parallelogram)
- is the height (the perpendicular distance from the base to the opposite side)
Worked Examples
Find the area of a parallelogram with base cm and height cm.
Write the formula
→ Area formula
Substitute the values
→ Plug in base and height
Calculate
→ cm²
Answer: The area is cm²
Common Mistakes
Using the slant side instead of the perpendicular height
Why it's wrong: The slant side is the length of the tilted edge, not the vertical distance between parallel sides.
Correct: Always look for the height that forms a 90° angle with the base. It's often shown with a small square symbol.
Forgetting to include square units in the answer
Why it's wrong: Area is always measured in square units because we're measuring two-dimensional space.
Correct: If base and height are in cm, the area is in cm². If in meters, the area is in m².
Multiplying all four sides together
Why it's wrong: Unlike perimeter (which uses all sides), area only needs base and height.
Correct: Use only two measurements:
Why It Matters
- Architecture: Parallelogram shapes appear in modern building designs and roof structures
- Art and Design: Many patterns and tiles use parallelogram shapes
- Physics: Forces and vectors often form parallelograms (parallelogram law)
- Foundation for other shapes: The parallelogram formula helps us understand the area of triangles, rhombuses, and other quadrilaterals
Real World Applications
Flooring and Tiles
Some decorative tiles are parallelogram-shaped. Knowing the area helps calculate how many tiles you need.
Example:
A parallelogram tile has a base of 20 cm and height of 15 cm. Each tile covers cm² = m².
You need to cover a floor of 6 m² with parallelogram tiles. Each tile has base 30 cm and height 20 cm.
How many tiles do you need?
Step 1: Write the mathematical expression
First find one tile's area, then divide:
Sail Design
Many sail shapes on boats approximate parallelograms. Calculating sail area is crucial for performance.
Example:
A sail with base 4 m and height 6 m has an area of m².
A boat needs 30 m² of sail area. The sail base is fixed at 5 m.
What height must the sail be?
Step 1: Write the mathematical expression
Rearrange to find :
Key Takeaways
- 1A parallelogram has opposite sides that are parallel and equal
- 2Area formula: (base times height)
- 3The height must be perpendicular (90°) to the base
- 4Don't confuse the slant side with the height
- 5Area is always expressed in square units (cm², m², etc.)
Frequently Asked Questions
Why doesn't the formula use the slant side?
Can I use any side as the base?
Is the area formula the same as for rectangles?
Glossary
- Parallelogram
- A four-sided polygon with two pairs of parallel sides
- Base
- Any side of the parallelogram chosen for calculating area
- Height
- The perpendicular distance from the base to the opposite side
- Perpendicular
- At a 90-degree angle
- Area
- The amount of space inside a two-dimensional shape, measured in square units