Geometry – Grade 8
Distinguish perimeter and area of rectangles and triangles, use correct units and calculate composite areas. Create a free worksheet or try an online test.
🎯 What you will learn
- ✓Distinguish perimeter from area
- ✓Choose the matching height and unit
💡 How it works
A fence needs the length around an edge; flooring needs the area inside. This lesson revisits rectangles, triangles and simple composite areas.
How it works
💡 Rectangle: U = 2(a + b), A = a × b. Triangle: A = g × h ÷ 2; h is perpendicular to g.
Perimeter U adds the outer side lengths. Area A counts unit squares inside. A rectangle measuring 8 cm by 5 cm has U = 26 cm but A = 40 cm². These results answer different questions.
A triangle has half the area of a parallelogram with the same base and height. Use the perpendicular height, not a sloping side. Split composite areas into familiar shapes; subtract any cut-out. For perimeter, count only the outer boundary, not internal construction lines.
🧩 See the method
✍️ Worked examples
Worked examples 1
Rectangle: a = 8 cm, b = 5 cm. U and A?
- 1.Boundary: 8 + 5 + 8 + 5 = 26 cm.
- 2.Inside area: 8 × 5 = 40 cm².
- 3.cm measures length; cm² measures area.
✓ U = 26 cm; A = 40 cm²
Worked examples 2
Triangle: g = 10 cm, h = 6 cm. A?
- 1.Use the base and its perpendicular height.
- 2.10 × 6 = 60 cm²; take half.
- 3.A = 60 ÷ 2 = 30 cm².
✓ 30 cm²
⚠️ Common mistakes
- • Giving an area in cm. Area needs square units such as cm².
- • Forgetting to halve the triangle’s area or using a sloping side as its height.
📝 Try it yourself
1.
Rectangle 7 cm × 3 cm: U?
Show answer
20 cm
2.
Rectangle 7 cm × 3 cm: A?
Show answer
21 cm²
3.
Square: side 6 cm. U?
Show answer
24 cm
4.
Triangle: g = 8 cm, h = 5 cm. A?
Show answer
20 cm²
5.
Rectangle 10 m × 6 m, cut-out 2 m × 3 m: remaining area?
Show answer
54 m²: 60 − 6
6.
2 m² = ? cm²
Show answer
20000
Create matching questions
Create a compact printable worksheet or start an online test.
Learn next
FAQ
Why is 1 m² not 100 cm²?
A 1 m × 1 m square is 100 cm × 100 cm. So 1 m² = 10000 cm².
Do shapes with equal perimeter have equal area?
Not necessarily. Rectangles 6 × 2 and 5 × 3 both have perimeter 16 but areas 12 and 15 in the appropriate units.