Finding the Area of a Rectangle

A rectangular garden is 8 meters long and 5 meters wide. What is its area?

Identify the dimensions: Length $l = 8$ m, Width $w = 5$ m = Dimensions identified

Write the formula: $\text{Area} = l \times w$ = Formula ready

Substitute the values: $\text{Area} = 8 \times 5$ = Values substituted

Calculate: $8 \times 5 = 40$ = $40 \text{ m}^2$

Answer: The garden has an area of $40 \text{ m}^2$

Finding the Area of a Triangle

A triangular sail has a base of 6 meters and a height of 4 meters. What is its area?

Identify the dimensions: Base $b = 6$ m, Height $h = 4$ m = Dimensions identified

Write the formula: $\text{Area} = \frac{1}{2} \times b \times h$ = Formula ready

Substitute the values: $\text{Area} = \frac{1}{2} \times 6 \times 4$ = Values substituted

Calculate step by step: $6 \times 4 = 24$, then $\frac{24}{2} = 12$ = $12 \text{ m}^2$

Answer: The sail has an area of $12 \text{ m}^2$

Rectangle with Decimal Dimensions

A picture frame is 12.5 cm long and 8 cm wide. Find its area.

Identify the dimensions: Length $l = 12.5$ cm, Width $w = 8$ cm = Dimensions identified

Apply the formula: $\text{Area} = 12.5 \times 8$ = Formula applied

Calculate: $12.5 \times 8 = 100$ = $100 \text{ cm}^2$

Answer: The picture frame has an area of $100 \text{ cm}^2$

Finding a Missing Dimension

A rectangle has an area of 48 square meters and a length of 8 meters. What is the width?

Write what we know: Area $= 48 \text{ m}^2$, Length $= 8$ m, Width $= ?$ = Information organized

Use the area formula: $48 = 8 \times w$ = Equation set up

Solve for width: $w = 48 \div 8$ = Division set up

Calculate: $w = 6$ = $6$ meters

Answer: The width is $6$ meters

Composite Shape: Rectangle Plus Triangle

A house wall has a rectangular base (10 m by 4 m) with a triangular roof section on top (base 10 m, height 3 m). Find the total area.

Find rectangle area: $10 \times 4 = 40 \text{ m}^2$ = Rectangle: $40 \text{ m}^2$

Find triangle area: $\frac{1}{2} \times 10 \times 3 = 15 \text{ m}^2$ = Triangle: $15 \text{ m}^2$

Add both areas: $40 + 15 = 55$ = $55 \text{ m}^2$

Answer: The total wall area is $55 \text{ m}^2$

Mistake: Using the slant side instead of the height for triangles

Why: 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.

Mistake: Forgetting to divide by 2 for triangle area

Why: A triangle is exactly half of a rectangle with the same base and height.

Correct: Remember: Triangle area = $\frac{1}{2} \times$ base $\times$ height. The $\frac{1}{2}$ is essential!

Mistake: Writing the wrong units (e.g., cm instead of cm²)

Why: Area measures two-dimensional space, so we need square units.

Correct: Always use square units: $\text{cm}^2$, $\text{m}^2$, $\text{in}^2$, etc.

Mistake: Confusing perimeter with area

Why: 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).

Painting a Room

Painters calculate wall area to know how much paint to buy.

A wall is 4 meters wide and 3 meters tall. Area = $4 \times 3 = 12 \text{ m}^2$. If one can of paint covers 10 m², you need 2 cans.

Designing a Triangular Banner

Event planners calculate fabric needed for decorative banners.

A triangular banner with base 2 m and height 1.5 m needs $\frac{1}{2} \times 2 \times 1.5 = 1.5 \text{ m}^2$ of fabric.

Laying Floor Tiles

Contractors calculate room area to order the right number of tiles.

A kitchen floor is 6 m by 4 m = 24 m². If each tile covers 0.25 m², you need 96 tiles.

Q: Why is triangle area half of rectangle area?

A: If you draw a rectangle and cut it diagonally, you get two identical triangles. Each triangle is exactly half the rectangle. That's why we multiply base × height (like a rectangle) and then divide by 2.

Q: What if the height is outside the triangle?

A: For obtuse triangles, the height may fall outside the triangle when you extend the base. The formula still works the same way - just make sure the height is perpendicular to the base (or its extension).

Q: Can I use any side as the base?

A: Yes! Any side of a triangle can be the base, but you must use the corresponding height (the perpendicular distance to that base). The area will be the same regardless of which side you choose.