What is a formula of trapezium?

A trapezium is a quadrilateral with only one pair of parallel sides. It is sometimes called a trapezoid. The formula to calculate the area of a trapezium is:

Area = (sum of the lengths of the parallel sides) multiplied by the height, divided by 2.

To use this formula, you need to know the lengths of both parallel sides as well as the height of the trapezium. The lengths of the parallel sides are the base1 and base2 of the trapezium.

Once you have the measurements, you can substitute them into the formula to find the area. Multiply the sum of the base1 and base2 by the height, and then divide the result by 2.

For example, let's say you have a trapezium with a base1 of 5 units, a base2 of 7 units, and a height of 10 units. The formula would look like this:

Area = (5 + 7) * 10 / 2

Simplifying the equation, we get:

Area = (12) * 10 / 2 = 120 / 2 = 60 square units.

Therefore, the area of the trapezium in this example would be 60 square units.

Remember that a trapezium is different from a rectangle or a square, as it has only one pair of parallel sides. Its formula takes into account this unique characteristic to calculate its area.

What is the formula for finding area of trapezium?

The formula for finding the area of a trapezium is:

Area = (base1 + base2) / 2 * height

A trapezium is a quadrilateral with only one pair of parallel sides. To find its area, you need to know the lengths of both bases and the height.

The formula works by:

Multiplying the sum of the lengths of the two bases by the height, and then dividing the result by 2. This accounts for the trapezium's unique shape, where it has two bases of different lengths.

For example:

Let's say we have a trapezium with base1 measuring 5 units, base2 measuring 7 units, and a height of 3 units. Using the formula:

Area = (5 + 7) / 2 * 3

Area = 12 / 2 * 3

Area = 6 * 3

Area = 18 square units.

Therefore, the area of the given trapezium is 18 square units.

It is important to note that:

The lengths of the bases and the height should be in the same unit of measurement. Ensure to label the sides correctly to avoid any confusion.

Using this formula, you can easily calculate the area of any trapezium given the necessary measurements.

What are the rules for a trapezium?

A trapezium is a quadrilateral with exactly one pair of parallel sides. It is a geometric shape that has several rules and properties.

The sum of the interior angles of a trapezium is always equal to 360 degrees. This means that when you add up all the angles inside a trapezium, the total will always be 360 degrees.

One of the defining properties of a trapezium is that the two non-parallel sides are of different lengths. This distinguishes a trapezium from a parallelogram, where opposite sides are equal in length.

A trapezium also has a unique property called the midsegment. The midsegment is the line segment that connects the midpoints of the two non-parallel sides. It is always parallel to the bases of the trapezium and its length is equal to the average of the lengths of the two bases.

Another important rule for a trapezium is the area formula. The area of a trapezium is given by the formula: Area = (1/2) × (sum of the lengths of the bases) × (height). The height is the perpendicular distance between the two bases.

Lastly, a trapezium can be classified as either an isosceles trapezium or a scalene trapezium. An isosceles trapezium has two sides of equal length, while a scalene trapezium has no equal sides.

In conclusion, a trapezium is a quadrilateral with one pair of parallel sides. Its interior angles sum up to 360 degrees, and it has two non-parallel sides of different lengths. The midsegment is parallel to the bases and has a length equal to the average of the lengths of the two bases. The area of a trapezium can be calculated using a specific formula, and it can be classified as either isosceles or scalene.

Why does the trapezium formula work?

Why does the trapezium formula work? This is a question often asked when studying calculus or numerical methods. The trapezium formula is a method used to approximate the definite integral of a function. It involves dividing the area under a curve into a series of trapezoids and summing up their areas. But why does this method work?

Firstly, it is important to understand the idea behind the trapezium rule. When we calculate the area under a curve, we approximate it by substituting the curve with a series of straight line segments. The trapezium rule takes this idea further by approximating the curve with trapezoids instead of straight lines. The formula for the area of a trapezoid is: (base1 + base2) x height / 2.

Now, let's consider a specific example. Suppose we have a function f(x) and we want to find the area under the curve between two points a and b. The trapezium rule divides this interval into n small segments, where the width of each trapezoid becomes (b - a)/n.

Next, the trapezium formula calculates the area of each trapezoid and sums them up to approximate the total area under the curve. It does this by finding the sum of the areas of the first trapezoid, the second trapezoid, and so on, until the last trapezoid. The formula used is: (f(a) + 2f(x1) + 2f(x2) + ... + f(b)) x (b - a) / (2n).

But why does this method work? The trapezium formula works because it provides a good approximation of the area under the curve by taking into account the slope of the curve at each point. By using trapezoids instead of straight lines, we are approximating the curve more accurately, especially when the curve is not a straight line itself.

Additionally, as we increase the number of trapezoids (or decrease the width of each trapezoid), the approximation becomes increasingly accurate. This is known as the principle of convergence. The more trapezoids we use, the closer our approximation gets to the actual value of the integral, and the smaller the error becomes.

In conclusion, the trapezium formula works because it approximates the area under a curve by dividing it into trapezoids and calculating their areas. By taking into account the slope of the curve, it provides a more accurate approximation than using straight lines. And by increasing the number of trapezoids, we can converge to the true value of the integral.

Is a trapezium 180 or 360?

Is a trapezium 180 or 360?

A trapezium is a quadrilateral with only one pair of parallel sides. The other two sides are called the legs, while the parallel sides are referred to as the bases. Determining the sum of the interior angles of a trapezium depends on the properties of its bases and legs.

Let's consider a trapezium with base angles of 90 degrees. In this case, the trapezium looks like a rectangle with one pair of opposite sides parallel. Since the sum of the interior angles in a rectangle is always 360 degrees, we can conclude that in this particular trapezium, the sum of the interior angles is also 360 degrees.

However, if the trapezium does not have base angles of 90 degrees, its interior angles differ. The non-parallel sides, or the legs, may have different lengths and angles, which affects the sum of the interior angles. In this case, the sum of the interior angles of a trapezium is always 180 degrees. This holds true regardless of the lengths or angles of the legs or bases.

In summary, a trapezium does not have a fixed sum of the interior angles like some other quadrilaterals. If the trapezium has base angles of 90 degrees, the sum of the interior angles is 360 degrees. Otherwise, the sum is always 180 degrees. It's important to consider the properties of the trapezium's bases and legs to determine the sum of its interior angles accurately.