Area of Rectangles and Triangles
Learn how to calculate the area of rectangles and triangles using simple formulas.
Definition
Rectangle Area Formula
Triangle Area Formula
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Worked Examples
A rectangular garden is 8 meters long and 5 meters wide. What is its area?
Identify the dimensions
Length m, Width m → Dimensions identified
Write the formula
→ Formula ready
Substitute the values
→ Values substituted
Calculate
→
Answer: The garden has an area of
Common Mistakes
Using the slant side instead of the height for triangles
Why it's wrong: The height must be perpendicular to the base. The slant side is usually longer than the actual height.
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 divide by 2 for triangle area
Why it's wrong: A triangle is exactly half of a rectangle with the same base and height.
Correct: Remember: Triangle area = base height. The is essential!
Writing the wrong units (e.g., cm instead of cm²)
Why it's wrong: Area measures two-dimensional space, so we need square units.
Correct: Always use square units: , , , etc.
Confusing perimeter with area
Why it's wrong: Perimeter is the distance around a shape (addition); area is the space inside (multiplication).
Correct: Perimeter = add all sides. Area = multiply dimensions (with formula adjustments for different shapes).
Interactive Visual
Triangle Explorer
Area:
20000.0 sq units
Drag the vertices to change the triangle shape.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
15 problemsA rectangle has a length of 6 cm and a width of 4 cm. What is its area?
Why It Matters
- Home Improvement: Calculating how much paint to buy for a wall or carpet for a floor
- Gardening: Determining how much soil or mulch you need for a garden bed
- Construction: Builders calculate roof area to order the right amount of shingles
- Art & Design: Artists plan canvas sizes and designers calculate space for layouts
Real World Applications
Painting a Room
Painters calculate wall area to know how much paint to buy.
Example:
A wall is 4 meters wide and 3 meters tall. Area = . If one can of paint covers 10 m², you need 2 cans.
You want to paint a rectangular wall that is 5 meters wide and 2.5 meters tall.
What is the area of the wall?
Step 1: Write the mathematical expression
Calculate:
Designing a Triangular Banner
Event planners calculate fabric needed for decorative banners.
Example:
A triangular banner with base 2 m and height 1.5 m needs of fabric.
You're making a triangular flag with a base of 80 cm and a height of 60 cm.
How much fabric do you need?
Step 1: Write the mathematical expression
Calculate:
Laying Floor Tiles
Contractors calculate room area to order the right number of tiles.
Example:
A kitchen floor is 6 m by 4 m = 24 m². If each tile covers 0.25 m², you need 96 tiles.
A bathroom floor is 3 meters by 2 meters. Each tile covers 0.5 m².
How many tiles do you need?
Step 1: Write the mathematical expression
First find area, then divide by tile size
Key Takeaways
- 1Area measures the space inside a flat shape, using square units (, , etc.)
- 2Rectangle area:
- 3Triangle area:
- 4The triangle's height must be perpendicular to the base
- 5Complex shapes can be broken into rectangles and triangles
Frequently Asked Questions
Glossary
- Area
- The amount of space inside a two-dimensional shape, measured in square units
- Square units
- Units used to measure area, like cm², m², or in²
- Base
- The bottom side of a shape, or any side chosen as the reference for calculating area
- Height
- The perpendicular distance from the base to the opposite vertex (for triangles) or side (for rectangles)
- Perpendicular
- At a right angle (90°) to another line or surface
Formula Card
Rectangle
$l$ = length, $w$ = width
Triangle
$b$ = base, $h$ = height