The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Area formulas to know
Area measures the space inside a flat shape, in square units. Rectangle: length × width. Triangle: ½ × base × height. Parallelogram: base × height.
The height must be measured straight up from the base (a right angle), not along a slanted side.
Area measures how much space a flat shape covers, in square units. Picture tiles on a floor. Each tile is one square unit.
Break complicated shapes into rectangles or triangles you already know how to measure, then add the pieces together.
Working an example
Plug the base and height into the formula, then simplify.
Find the area of a triangle with base 10 cm and height 6 cm.
- 1A = ½ × base × height.
- 2A = ½ × 10 × 6.
- 3A = 30 cm².
Why this matters
The space inside flat shapes - rectangles, triangles, and parallelograms.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Area formulas to know
- Working an example
Video walkthroughs
Area of Triangles Intuition
See why triangle area is one-half base times height.
Watch on YouTube
Area of an Isosceles Triangle
Find triangle area using base, height, and the area formula.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfFind the area of a rectangle 9 cm long and 4 cm wide.
Step-by-step solution
- 1A = length × width.
- 2A = 9 × 4 = 36 cm².
Exercise 2
Try it yourselfFind the area of a triangle with base 8 m and height 5 m.
Step-by-step solution
- 1A = ½ × base × height.
- 2A = ½ × 8 × 5 = 20 m².
Exercise 3
Try it yourselfFind the area of a parallelogram with base 12 in and height 7 in.
Step-by-step solution
- 1A = base × height = 12 × 7.
- 2A = 84 in².
Exercise 4
Try it yourselfA trapezoid has parallel sides 6 cm and 10 cm and height 4 cm. Find its area.
Step-by-step solution
- 1A = ½ × (b₁ + b₂) × h.
- 2A = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 cm².
Exercise 5
Try it yourselfA triangle has area 54 ft² and base 12 ft. Find the height.
Step-by-step solution
- 154 = ½ × 12 × h → 54 = 6h.
- 2h = 54 ÷ 6 = 9 ft.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Area of Triangles & Quadrilaterals
Question 1 of 5
What is the area of a triangle with base 10 cm and height 6 cm?