Area of a Trapezoid
(KS3, Year 7)
The LessonThe area of a trapezoid is found using the formula:
In this formula, b1 and b2 are the lengths of the bases of the trapezoid and h is the height of the trapezoid. The image below shows what we mean by the lengths of the bases and the height:
How to Find the Area of a TrapezoidFinding the area of a trapezoid is easy.
QuestionWhat is the area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm, as shown below?
Start with the formula:
Area = ½(b1 + b2)hDon't forget: ½(b1 + b2)h = ½ × (b1 + b2) × h
Substitute the length of the bases and the height into the formula. In our example, b1 = 3, b2 = 5 and h = 3.
Area = ½ × (3 + 5) × 2 Area = ½ × (8) × 2 Area = 8 cm2Don't forget: Calculate what's in the brackets () first (using the order of operations). In our example, (3 + 5) = 8. or: ½ × a number = 0.5 × a number = a number ÷ 2.
Answer:The area of a trapezoid with bases of length 3 cm and 5 cm and a height of 2 cm is 8 cm2.
"Find the Area" Widget
- Click on the shape you're learning about.
- Click on the pad to start.
- Follow the instructions in the bottom-left corner.
- On the last click, the formula, workings, and answer will appear in the yellow box.
- Good luck!
Lesson SlidesThe slider below shows another real example of how to find the area of a trapezoid. Open the slider in a new tab
I Say Trapezoid, You Say TrapeziumThe shape is called a trapezoid in North America. In English speaking countries outside North America, a trapezoid is called a trapezium.
What Is a Trapezoid?A trapezoid is a four-sided flat shape with straight sides. It has a pair of opposite sides which are parallel.
A Note on UnitsThe area of a trapezoid is a length times a length, so we say its dimension is length2. (All areas are lengths squared). This affects the units used. If the lengths of a rectangle are in cm, the area is in cm2. If the lengths are in inches, the area is in inches2.
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