Study guides › Level 7 · Geometry

Areas of triangles, trapezoids and parallelograms

Level 7 · Geometry · for questions like “A garden bed is a trapezoid with parallel sides of 6 m and 10 m, 4 m apart. What is its area?”

💡 The idea

• Parallelogram: base × height.
• Triangle: ½ × base × height (half a parallelogram).
• Trapezoid: the average of the two parallel sides × the height.

The height is always measured straight up, at a square angle to the base, never along a slanted side.

✏️ Worked examples

1. Trapezoid 6 and 10, height 4: (6 + 10) ÷ 2 × 4 = 32 sq m.

2. Triangle, base 12 and height 5: ½ × 12 × 5 = 30.

3. Parallelogram, base 9 and height 4 (slanted sides 5): 9 × 4 = 36. The 5 isn't needed.

⚠️ Watch out

• Ignore the slanted side for area.
• Don't forget the ½ for triangles.

🎯 Try these

1. Triangle, base 10 and height 7
2. Trapezoid 5 and 9, height 6
3. Parallelogram, base 11 and height 3

Answers: 1) 35 2) 42 3) 33

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.