Area of a Trapezium
The area of a trapezium is (a + b) ÷ 2 × h, where a and b are the parallel sides and h is the perpendicular height, not the slanted side. With bases 8 cm and 12 cm and height 6 cm: (8 + 12) ÷ 2 × 6 = 10 × 6 = 60 cm².
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What is a Trapezium?
- A trapezium is a four-sided shape with only one pair of parallel sides.
- The height is the perpendicular distance between the parallel sides.
Area of a Trapezium
- The area of a trapezium is given by: Area
- Here, a and b are the lengths of the parallel sides.
Area of a Right-Angled Trapezium
- A right-angled trapezium has two right angles, so the height is easy to identify.
- Use the same formula and take the perpendicular side as the height.
Finding the Height of a Trapezium
- Use the same formula: Area
- Substitute the known values and solve for the height.
Practice Questions
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Which of the following is always true for a trapezium?
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A trapezium is defined as a quadrilateral with exactly one pair of parallel sides. Two pairs would make it a parallelogram.
What is the height of a trapezium?
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The height is always the perpendicular distance between the two parallel sides, not a slanted or longest side.
Calculate the area of a trapezium with parallel sides and , and height .
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Use the formula: Area . cm².
In a right-angled trapezium, the shorter base is , the longer base is , and the area is . What is the height?
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. , so . Height cm.
An isosceles trapezium has parallel sides of and . If its area is , what is the height?
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. , so height cm.
Find the area of the isosceles trapezium shown, where the bottom base is , the top base is , and the height is .
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Area cm².
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The formula for the area of a trapezium is (a + b) ÷ 2 × h. Here, a and b are the lengths of the two parallel bases. The letter h is the perpendicular height. You add the two bases, divide by 2, then multiply by the height to get the area in squared units.
A trapezium has exactly one pair of parallel sides, while a parallelogram has two pairs of parallel sides. If both pairs of opposite sides in a four-sided shape run parallel, the shape is a parallelogram, not a trapezium. This distinction matters because the two shapes use different area formulas.
Yes. A right-angled trapezium has exactly two right angles. One of its non-parallel sides meets both bases at 90°, forming a perpendicular side. This perpendicular side also acts as the height, making it easier to identify the correct measurement for the area formula.
The height of a trapezium must be the perpendicular distance between the two parallel bases. The slanted sides are not perpendicular to the bases, so using them gives an incorrect measurement. Always look for or draw a line at a right angle to both bases to find the true height.
A trapezium has four sides, making it a quadrilateral. Two of these sides are parallel and are called the bases. The other two sides are not parallel. Every trapezium shares this four-sided structure, whether it is right-angled, isosceles, or a general trapezium.
Rearrange the area formula by first adding the two parallel bases and dividing by 2. Then divide the area by that result. For example, if the bases are 5 m and 9 m with an area of 21 m², you calculate (5 + 9) ÷ 2 = 7, then 21 ÷ 7 = 3 m.