P5 Area of Triangle: Master Base & Height

Confused about which side is the base and which is the height? You’re not alone! Let’s master the “T-Rule” and ace those P5 Geometry questions.

The “T-Rule”: Identifying Base and Height

The most important rule in finding the area of a triangle is identifying the correct base and height. Many students make the mistake of just picking any two numbers they see.

The Golden Rule: The Base and Height must typically form a “T” shape. They must be perpendicular (meet at a right angle/90°).

💡 The 90° Check

Always look for the small square symbol (right-angle marker). That symbol connects your Base and Height!

Visualizing the Connection

Let’s look at a right-angled triangle. Here, the two sides that make the right angle are automatically the base and height.

In a right-angled triangle, the two perpendicular sides are the base (8cm) and height (6cm).

The Formula: Why 1/2?

You already know that the Area of a Rectangle is $Length \times Breadth$ .

But did you know that every triangle is exactly half of a rectangle?

$Area = \frac{1}{2} \times Base \times Height$

⚠️ Don't Forget the 1/2!

The most common careless mistake is forgetting to multiply by $\frac{1}{2}$ . Students often just multiply Base $\times$ Height. Remember: it’s a triangle, not a rectangle!

Worked Examples

Let’s apply the formula to some problems.

Example 1: Standard Triangle

Finding Area Given Base and Height

Problem:

Find the area of a triangle with a base of 12 cm and a height of 8 cm.

Step 1: Identify Base and Height

Base = 12 cm, Height = 8 cm

Step 2: Apply the Formula

$Area = \frac{1}{2} \times Base \times Height$

$Area = \frac{1}{2} \times 12 \times 8$

$Area = 6 \times 8$

$Area = 48 \text{ cm}^2$

Example 2: The “Hidden” Height

Sometimes, especially in obtuse triangles, the height is drawn outside the triangle. Does the formula change? No!

Height Outside the Triangle

Problem:

An obtuse triangle has a base of 6 m. Its height is 10 m, drawn outside the triangle. Find its area.

Step 1: Identify Base and Height

Base = 6 m (Note: Only use the length of the triangle’s side, not the extended part!)

Height = 10 m

Step 2: Apply the Formula

$Area = \frac{1}{2} \times 6 \times 10$

$Area = 3 \times 10$

$Area = 30 \text{ m}^2$

Common Mistakes to Avoid

Using the Slanted Side as Height: Height is always the straight vertical distance (perpendicular), never the slanted side unless it’s a right-angled triangle.
Including the Extension: When height is outside, students sometimes add the “dotted line” part to the base. The base is ONLY the solid line of the triangle.
Forgetting Units: Area is always in square units ( $cm^2, m^2$ ), not length units ( $cm, m$ ).

Ready to Practice?

Mastering the Area of Triangle is key for P5 and P6 math. Once you get comfortable with identifying the base and height, the calculation is simple!

Try It Yourself!

Practice finding the area of different triangles types on HomeCampus.

Start Practicing P5 Area →

P5 Area of Triangle: The Complete Guide to Base & Height