Area of a trapezium: Class 8 practice
A trapezium has one pair of parallel sides. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Area of rectangle and triangle
The idea behind area of a trapezium
A trapezium has one pair of parallel sides. Its area is half the sum of the parallel sides times the distance between them: A = ½(a + b)h.
Step-by-step method
- Identify the parallel sides a and b.
- Find the perpendicular height h.
- A = ½(a + b) × h.
- To find h: h = 2A ÷ (a + b).
Worked example 1 (Basic)
Find the area of a trapezium with parallel sides 18 cm and 25 cm and height 8 cm.
- A = ½ × (18 + 25) × 8
- A = 172 cm²
- Answer: 172 cm²
Worked example 2 (Standard)
Find the area of a trapezium with parallel sides 15 cm and 20 cm and height 22 cm.
- A = ½ × (15 + 20) × 22
- A = 385 cm²
- Answer: 385 cm²
Worked example 3 (Challenge)
A trapezium-shaped field has area 176 m² and parallel sides 20 m and 24 m. Find the distance between them.
- h = 2 × 176 ÷ (20 + 24)
- h = 8 m
- Answer: 8 m
Common mistakes and misconceptions
- Using a slant side as the height
- Forgetting the ½
Practice questions
- (Basic) Find the area of a trapezium with parallel sides 7 cm and 18 cm and height 14 cm.
- (Basic) Find the area of a trapezium with parallel sides 13 cm and 27 cm and height 8 cm.
- (Standard) Find the area of a trapezium with parallel sides 13 cm and 14 cm and height 12 cm.
- (Standard) Find the area of a trapezium with parallel sides 20 cm and 22 cm and height 6 cm.
- (Challenge) A trapezium-shaped field has area 192 m² and parallel sides 14 m and 18 m. Find the distance between them.
- (Challenge) A trapezium-shaped field has area 171 m² and parallel sides 8 m and 11 m. Find the distance between them.
Answer key with full working
- Q1: A = ½ × (7 + 18) × 14 → A = 175 cm² → Answer: 175 cm²
- Q2: A = ½ × (13 + 27) × 8 → A = 160 cm² → Answer: 160 cm²
- Q3: A = ½ × (13 + 14) × 12 → A = 162 cm² → Answer: 162 cm²
- Q4: A = ½ × (20 + 22) × 6 → A = 126 cm² → Answer: 126 cm²
- Q5: h = 2 × 192 ÷ (14 + 18) → h = 12 m → Answer: 12 m
- Q6: h = 2 × 171 ÷ (8 + 11) → h = 18 m → Answer: 18 m
Syllabus note
This skill is listed under "Mensuration" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is area of a trapezium in?
"Mensuration", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.