The lesson
This lesson teaches Area of Triangles & Quadrilaterals. 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.
When you study working an example, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
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
Area of Triangles & Quadrilaterals shows up constantly in the space inside flat shapes - rectangles, triangles, and parallelograms. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Area formulas to know
- Working an example
Video walkthrough
Practice
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?