Finding Area of Triangles and Parallelograms

What you'll learn

In this lesson, you'll learn how to find the area of triangles and parallelograms, and understand why each formula works by connecting it back to the area of a rectangle.

Why this matters

Area of triangles and parallelograms shows up in construction, art, land measurement, and design — anywhere a shape isn't a simple rectangle.

Concept/foundation recap

Area of a rectangle = base × height. A parallelogram can be reshaped into a rectangle by cutting a triangle off one end and moving it to the other — same base, same height, same area. A triangle is exactly half of a parallelogram that shares its base and height.

Visualizing the concept

Two views: a parallelogram being cut and rearranged into a rectangle, and two identical triangles combining to form a parallelogram.

The rule / method (and why it works)

• Parallelogram: Area = base × height

• Triangle: Area = 1/2 × base × height (because a triangle is half of a matching parallelogram)

Step-by-step worked examples

• Example 1: Parallelogram with base = 10 units, height = 6 units → Area = 60 square units

  

  
  

• Example 2: Triangle with base = 8 units, height = 5 units → Area = 20 square units

Try it together (Parent + Child)

Find a triangle or parallelogram shape at home — a cut sandwich, a slice of pizza, a picture frame mat. Measure its base and height and calculate the area together.

Parent prompt: "Which measurement is the base, and which is the height?"

Independent practice

Students calculate the area of several triangles and parallelograms from given base and height measurements, and explain which formula they used and why.

Common mistakes to avoid

• Using the slanted side instead of the true height (height must be perpendicular to the base)

• Forgetting to multiply by 1/2 for triangles

• Mixing up which measurement is the base and which is the height

If you can explain why a triangle's area is half of a parallelogram's, you understand this lesson.