Area of Triangles and Trapezoids
Triangles take half of a base × height box.
About this topic
The area of a triangle is half the base times its perpendicular height, A = ½bh, since two copies make a parallelogram. A trapezoid has one pair of parallel sides (bases), and its area is A = ½(b₁ + b₂)h, the average of the bases times the height.
Heron's formula finds a triangle's area from its three sides alone. Always use the perpendicular height, not a slanted side. These formulas are used in land measurement, roofing and engineering.
Worked example: a triangle has base 10 and height 6, so its area is ½ × 10 × 6 = 30. A trapezoid with bases 7 and 11 and height 4 has area ½(7 + 11)(4) = 36. For Heron's formula, sides 5, 6, 7 give s = 9 and area √(9 × 4 × 3 × 2) = √216 ≈ 14.7. In a right triangle you can use the two legs as base and height.
Roof surveyors and land owners use these formulas to measure irregular plots by splitting them into triangles. The classic mistake is using a slanted side as the height; the height must be perpendicular to the chosen base and may lie outside an obtuse triangle. Also, students forget the ½ in the triangle formula or the average of both bases in the trapezoid. If your triangle's area looks twice what a quick sketch suggests, you probably omitted the one half.
Key ideas
- Triangle: ½bh
- Trapezoid: ½(b₁ + b₂)h
- Heron's formula uses three sides
Quick check
Use cases: where Area of Triangles and Trapezoids helps
- Homework: review the key idea behind Area of Triangles and Trapezoids before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Area of Triangles and Trapezoids without notes.
- Visual learning: play with the interactive lab to see how Area of Triangles and Trapezoids changes when you adjust its inputs.
- Teaching a friend: explain Area of Triangles and Trapezoids in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Area of Triangles and Trapezoids?
Triangles take half of a base × height box.
What will I learn in Area of Triangles and Trapezoids?
Triangle: ½bh. Trapezoid: ½(b₁ + b₂)h. Heron's formula uses three sides.
Is Area of Triangles and Trapezoids part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Area of Triangles and Trapezoids lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Area of Triangles and Trapezoids?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
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