Understanding the formula for the area of a trapezium – To find the area of a trapezium:

- Draw two trapeziums.
- Rotate one trapezium by 180°.
- Put the two trapeziums together to form a parallelogram.
- The area of the parallelogram is the base multiplied by the perpendicular height. The base of the parallelogram is the total of the two parallel sides of the trapezium, (𝒂 + 𝒃). The area of the parallelogram is (𝒂 + 𝒃)𝒉.
- The area of the trapezium is half of the area of the parallelogram. The formula is ½(𝒂 + 𝒃)𝒉.

When the trapezium has two right angles, the two congruent trapeziums make a rectangle. The formula for the area (𝑨) of a trapezium is 𝑨=½ (𝒂 + 𝒃)𝒉.1 of 9 Draw two congruent (identical) trapeziums.2 of 9 Rotate one trapezium by 180° and put the two trapeziums together to form a parallelogram. The base of the parallelogram is the total length of the parallel sides of the trapezium, 𝒃 + 𝒂 = 𝒂 + 𝒃. The perpendicular height of the parallelogram is the height (𝒉) of the trapezium.3 of 9 The area of the parallelogram is the base multiplied by the height. (𝒂 + 𝒃) × 𝒉. This can be written without the multiplication symbol as (𝒂 + 𝒃)𝒉 4 of 9 The area of the trapezium is half of the area of the parallelogram. The formula can be written as 𝑨 = ½ (𝒂 + 𝒃)𝒉 or 𝑨 = (𝒂 + 𝒃)𝒉/2 5 of 9 When the trapezium has two right angles, two congruent trapeziums can be put together to make a rectangle.6 of 9 To use the formula 𝑨 = ½ (𝒂 + 𝒃)𝒉, the parallel sides and the perpendicular height must be identified.7 of 9 The parallel sides are always on opposite sides of the trapezium. They are the same distance apart throughout their length.8 of 9 The height is the shortest distance between the parallel sides. The height meets the parallel sides at right angles.9 of 9

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#### What is the formula for finding area of a trapezium?

Area = (1/2) h (a+b) a and b are the length of parallel sides/bases of the trapezium. h is the height or distance between parallel sides.

## How to calculate area?

Areas of Simple Quadrilaterals: Squares and Rectangles and Parallelograms – The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. Area of a rectangle = height × width For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. Often, in real life, shapes can be more complex. For example, imagine you want to find the area of a floor, so that you can order the right amount of carpet. A typical floor-plan of a room may not consist of a simple rectangle or square: In this example, and other examples like it, the trick is to split the shape into several rectangles (or squares). It doesn’t matter how you split the shape – any of the three solutions will result in the same answer. Solution 1 and 2 require that you make two shapes and add their areas together to find the total area.

#### What is an area calculator?

Area calculator helps to find size of the surface of all-important geometry flat shapes like (Triangle, Rectangle, Square, Circle, Sector, Parallelogram etc) in major measure units (inches, meters, centimeters, yards, kilometers, feet etc).

#### What is the formula for area called?

Rectangles – The area of this rectangle is lw, The most basic area formula is the formula for the area of a rectangle, Given a rectangle with length l and width w, the formula for the area is: A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width.

## What is trapezoid called in UK?

As a teacher, I remember endlessly talking about squares in the same breath as saying “squares are a special type of rectangle”. I often designed activities that resulted in pupils producing tree or Venn diagrams to show the family classifications of quadrilaterals.

Whether it was angles, dimensions, measures, constructions, or to represent unknown quantities, shapes could regularly be seen in lessons. As I design the geometry waypoints in the Cambridge Mathematics Framework I have found a large amount of research concerning the classification of quadrilaterals.

Much of this research identifies issues that we’re all too familiar with: pupils not recognising that a square is a type of rectangle and a rectangle a type of parallelogram; the necessary and sufficient properties a quadrilateral and the characteristics of the shapes to list a few.

- Pupils rarely fully understand or know a true mathematical definition for each quadrilateral, and instead tend to list their characteristics, four sides and all.
- A few specifics stick out.
- Some muddy the waters while others help us to clear up the problems.
- With that in mind, here’s a small selection of important issues to think about when you’re working in this area.

What is the definition of a trapezium? Is it a shape with exactly one pair of parallel sides or at least one pair of parallel sides? Or maybe even none at all! Different cultures define a trapezium slightly differently and many have the term trapezoid too.

In the US (for some) a trapezium is a four sided polygon with no parallel sides ; in the UK a trapezium is a four sided polygon with exactly one pair of parallel sides ; whereas in Canada a trapezoid has an inclusive definition in that it’s a four sided-polygon with at least one pair of parallel sides – hence parallelograms are special trapezoids.

Now I’m not in a position to make a definitive decision on this – but pointing out that these issues exist (especially in the multicultural classrooms in which we teach) is essential, as is pointing out to those who search the internet when lesson planning that some care, attention and scepticism is often needed! Euclid, the forefather to much of our school geometry curriculum, defined (Book 1, Definition 2) a square to have equal sides and right angles, an oblong to have four right angles but not four equal sides, a rhombus to have four equal sides but no right angles, a rhomboid to have equal opposite sides and equal opposite angles but without right angles and without four equal sides.

All other quadrilaterals were trapezia. Even just making sense of this is a great opportunity to really think about what these shapes look like and their familiar relationships as Euclid implies that there are in fact no intersections at all between shapes. Each is either a square, an oblong, a rhombus, a rhomboid or trapezia.

Now wouldn’t that make life simpler? Well yes and no. A question to ask yourself is why do we have the inclusive definitions we do? What’s the point – surely they just daze and confuse? It all comes down to what we can deduce and infer from one shape to another.

- A square is a special type of rectangle and rhombus and therefore a special parallelogram.
- These hierarchical definitions lead to more economical definitions of concepts and formulation of theorems, simplify the deductive systematization and derivation of the properties of more special concepts, provide useful conceptual schema during problems solving, can suggest alternative definitions and new propositions and provide useful global perspectives (De Villiers, 1994).

In other words: a theorem you prove for a parallelogram holds for squares, rectangles, and rhombi as they are all types of parallelogram. Yet a theorem that holds for a square may not hold for all parallelograms as not all parallelograms are squares. At this point it’s really interesting to look at the restrictions needed as you pass around the family of parallelograms; to consider what remains invariant and how this interacts with the theorem in question. https://upload.wikimedia.org/wikipedia/commons/9/9a/Euler_diagram_of_quadrilateral_types.svg You may not completely agree with the names being used, but what’s wonderful is how you can identify the tightening or loosening restriction as you take a walk around.

Leave a region and you loosen, enter another layer and you tighten. It also highlights that actually, you know what, maybe oblong isn’t such a nasty word – oblongs and squares make up the rectangle family and ‘oblong’ might help with the whole squares are rectangles confusion. Alternatively, Clements and Sarama (2009) suggest using the double name square-rectangle.

Would this mean we would also have rhombus-parallelograms? It would be nice to consider if some regions are actually empty and as a team we have a question as to whether ‘darts’ here should be encompassed in the kite region too? The whole conversation just highlights how confusing defining quadrilaterals can be.

Crucially we need to decide on what we consider to be necessary and sufficient conditions, and therefore familiar relationships, whilst at the same time being ready to state them explicitly. Maybe once we’ve done that we can draw our own Wikipedia diagram for our definitions. I’ll leave that once with you, but I would be interested in what you design! Can I uncover your definitions from your diagram? References: Clements, D.H., Sarama, J., 2000.

Young Children’s Ideas About Geometric Shapes. Teaching Children Mathematics 6, 482–488. De Villiers, M., 1994. The role and function of a hierarchical classification of quadrilaterals. For the learning of mathematics 14, 11–18. Sarama, J., Clements, D.H., 2009. KS2: A rectangle is a special type of parallelogram. Why? KS3: Draw a tree diagram to link the family of quadrilaterals. Explain the links you have made. KS4: Construct a cyclic parallelogram. KS5: Van Aubel’s theorem states that: If squares are constructed on the sides of any quadrilateral, then the line segments connecting the centres of opposite squares are equal and perpendicular.

#### Is a trapezoid British or American?

In geometry, a trapezoid (/ˈtræpəzɔɪd/) in American and Canadian English, or trapezium (/trəˈpiːziəm/) in British and other forms of English, is a quadrilateral that has at least one pair of parallel sides.

#### What’s a 3D trapezoid called?

Why is the Trapezoidal Prism a 3D Figure? – The 3D figure of a trapezoid is called a trapezoidal prism since these are figures that have a length, width, and depth. The edges of the prism is where the faces meet, and the vertices of the prism are the corners where three or more surfaces meet.

#### What are two examples of trapezium?

A trapezium is a two-dimensional geometrical figure which consists of one pair of sides that are parallel to each other. We can see various real-life examples of the shape of a trapezium, some of which are buckets, suitcases, popcorn boxes, etc. The word ‘trapezium’ has its origin from the word ‘trapeze’, a Greek word, the meaning of which is the table.

This two-dimensional geometrical figure can be classified as a quadrilateral whose opposite parallel sides are known as the bases of the trapezium and the other two remaining sides are known as the legs of the trapezium. In this article, we will discuss the area of a trapezium, various types of the trapezium, and also discuss some of the important properties related to the quadrilateral along with solving some examples.

The total area that is occupied by a trapezium is known as the area of a trapezium. Calculation of the area of a trapezium is very easy. We can calculate it by obtaining the average of the two bases of the trapezium and then multiplying it with its altitude.

## What is an example of a trapezoid?

14. A trapezoid chair back: – It refers to a chair backrest that has a trapezoidal shape. A trapezoid is a quadrilateral with two parallel sides, which means that a trapezoid chair back has two sides that are parallel to each other, while the other two sides are not parallel.