Area of trapezium

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Finding the area of various shapes like trapeziums may sound difficult in the start due to their forms. However, all you need is the right formula to calculate the area of a trapezium. The area covers a dimensional space that it occupies. In this article, we’ll define what a trapezium is and show you different ways to find the area. Euclid wrote his geometry work about 300 B.C. in his book; he did use the word trapezion, as the name of a four-sided figure that wasn’t a rhomboid, rectangle or a rhombus. The name later got a Latin translation to now the trapezium. Later, Proclus a geometer incorporated specific refinements to Euclid’s work, which have now become geometry basics. Proclus came up with a new meaning of a trapezium, where he referred to it as any four-sided figure with two parallel sides. The geometer later came up with a new term, trapezoid which denotes a four-sided figure with no two parallel sides. However, in 1795, an English mathematician, Charles Hutton got the descriptions reversed. The US still follows the Hutton’s definition although the British have reverted to Proclus original meaning. For you to calculate the area of a trapezium, you need to have a formula. Find the length of the nonparallel side, the height of the trapezoid, and the length of one base. The height of a trapezoid is the diagonal line that extends from one corner to another opposite edge. The basic formula is (B1+B2) x1/2x (H) Also, you can get the area of a trapezoid by dividing it i...

Trapezoid (Jump to A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel (marked with arrows below): Trapezoid Isosceles Trapezoid A trapezoid: has a pair of is an isosceles trapezoid when it has equal angles from a parallel side is called a " trapezium" in the UK (see Play with a trapezoid: Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what is its Perimeter? Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = 36 cm Median of a Trapezoid The median (also called a midline or midsegment) is a line segment half-way between the two bases. The median's length is the average of the two base lengths: m = a+b 2 You can calculate the area when you know the median, it is just the median times the height: Area = mh Trapezium A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides. The US and UK have their definitions swapped over, like this: Trapezoid Trapezium US: a pair of parallel sides NO parallel sides UK: NO parallel sides a pair of parallel sides

More things to try: • • • References Beyer, W.H. (Ed.). Bronshtein, I.N. and Semendyayev, K.A. Harris, J.W. and Stocker, H. "Trapezoid."§3.6.2 in Kern, W.F. and Bland, J.R. Cite this as: MathWorld--A Wolfram Web Resource. Subject classifications • • • • • • • • • • • • • • • • • • • • Created, developed and nurtured by Eric Weisstein at Wolfram Research

What is a trapezoid? A trapezoid or trapezium is a quadrilateral with at least one pair of parallel sides. The parallel sides are known as bases. When the other two sides are non-parallel, they are called legs or lateral sides. Else there are two pairs of bases. Real-life examples where you can see the area of trapezoids are handbags, popcorn tins, and the guitar-like dulcimer. The area of a trapezoid is the complete space enclosed by its four sides. There are two approaches to finding the area of trapezoids. • The first method is a direct method that uses a direct formula to find the area of a trapezoid with the known dimensions (see example 1) • For the second method, firstly, if we are given the length of all the sides, we split the trapezoid into smaller polygons such as triangles and rectangles. Next, we will find the What is the Formula To Calculate the Area of Trapezoids? We can calculate the area of trapezoid if we know the length of its parallel sides and the distance (height) between the parallel sides. The area of trapezoids formula is: ‘h’ is the height, i.e., the perpendicular distance between the parallel sides. Area of Trapezoid Example Here is an area of a trapezoid example using the direct formula and an area of a trapezoid example with the alternative method. Example 1: Find the area of a trapezoid given the length of parallel sides 22 cm and 12 cm, respectively. The height is 5 cm. Solution: Given: The bases are : a = 22 cm; b = 10 cm; the height is h = ...

Trapezoidal Prism A trapezoidal prism is a 3D figure made up of two trapezoids that is joined by four rectangles.Prisms consist of polygons that form their bases. One of the most recognizable examples of a trapezoid prism is a brick especially the circular fire pit brick. A trapezoidal prism comes from the shape trapezoid. Let's learn more about itsdefinition, properties, formulas and solve a few examples. 1. 2. 3. 4. 5. 6. TrapezoidalPrism Properties The properties of a trapezoid prism are very similar to that of a • A trapezoid prism consists of two trapezoids that are joined by four rectangles • A trapezoid prism consists of eight vertices • A trapezoid prism consists of six faces • A trapezoid prism consists of 12 edges • A trapezoid prism is a polygon that consists of trapezoids Trapezoidal Prism Net The net of the trapezoidal prism consists of six faces, eight vertices, and 12 edges. When the trapezoidal prism is opened flat, we can see the four rectangle-shaped objects that help in joining the two trapezoid-shaped objects together to form a trapezoidal prism. The image below demonstrates the flattened version of a trapezoidal prism. Surface Area of a Trapezoidal Prism The surface Surface Area of a Trapezoidal Prism =h (b + d) + l (a + b + c + d) square units where h is the height, b and d are the lengths of the base, a + b + c + d is the Related Topics Listed below are a few interesting topics related to the trapezoidal prism. • • • • Example 1: Sandy is setting up ...

Trapezoidal Prism A trapezoidal prism is a 3D figure made up of two trapezoids that is joined by four rectangles.Prisms consist of polygons that form their bases. One of the most recognizable examples of a trapezoid prism is a brick especially the circular fire pit brick. A trapezoidal prism comes from the shape trapezoid. Let's learn more about itsdefinition, properties, formulas and solve a few examples. 1. 2. 3. 4. 5. 6. TrapezoidalPrism Properties The properties of a trapezoid prism are very similar to that of a • A trapezoid prism consists of two trapezoids that are joined by four rectangles • A trapezoid prism consists of eight vertices • A trapezoid prism consists of six faces • A trapezoid prism consists of 12 edges • A trapezoid prism is a polygon that consists of trapezoids Trapezoidal Prism Net The net of the trapezoidal prism consists of six faces, eight vertices, and 12 edges. When the trapezoidal prism is opened flat, we can see the four rectangle-shaped objects that help in joining the two trapezoid-shaped objects together to form a trapezoidal prism. The image below demonstrates the flattened version of a trapezoidal prism. Surface Area of a Trapezoidal Prism The surface Surface Area of a Trapezoidal Prism =h (b + d) + l (a + b + c + d) square units where h is the height, b and d are the lengths of the base, a + b + c + d is the Related Topics Listed below are a few interesting topics related to the trapezoidal prism. • • • • Example 1: Sandy is setting up ...

Trapezoid (Jump to A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel (marked with arrows below): Trapezoid Isosceles Trapezoid A trapezoid: has a pair of is an isosceles trapezoid when it has equal angles from a parallel side is called a " trapezium" in the UK (see Play with a trapezoid: Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what is its Perimeter? Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = 36 cm Median of a Trapezoid The median (also called a midline or midsegment) is a line segment half-way between the two bases. The median's length is the average of the two base lengths: m = a+b 2 You can calculate the area when you know the median, it is just the median times the height: Area = mh Trapezium A trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides. The US and UK have their definitions swapped over, like this: Trapezoid Trapezium US: a pair of parallel sides NO parallel sides UK: NO parallel sides a pair of parallel sides

More things to try: • • • References Beyer, W.H. (Ed.). Bronshtein, I.N. and Semendyayev, K.A. Harris, J.W. and Stocker, H. "Trapezoid."§3.6.2 in Kern, W.F. and Bland, J.R. Cite this as: MathWorld--A Wolfram Web Resource. Subject classifications • • • • • • • • • • • • • • • • • • • • Created, developed and nurtured by Eric Weisstein at Wolfram Research

What is a trapezoid? A trapezoid or trapezium is a quadrilateral with at least one pair of parallel sides. The parallel sides are known as bases. When the other two sides are non-parallel, they are called legs or lateral sides. Else there are two pairs of bases. Real-life examples where you can see the area of trapezoids are handbags, popcorn tins, and the guitar-like dulcimer. The area of a trapezoid is the complete space enclosed by its four sides. There are two approaches to finding the area of trapezoids. • The first method is a direct method that uses a direct formula to find the area of a trapezoid with the known dimensions (see example 1) • For the second method, firstly, if we are given the length of all the sides, we split the trapezoid into smaller polygons such as triangles and rectangles. Next, we will find the What is the Formula To Calculate the Area of Trapezoids? We can calculate the area of trapezoid if we know the length of its parallel sides and the distance (height) between the parallel sides. The area of trapezoids formula is: ‘h’ is the height, i.e., the perpendicular distance between the parallel sides. Area of Trapezoid Example Here is an area of a trapezoid example using the direct formula and an area of a trapezoid example with the alternative method. Example 1: Find the area of a trapezoid given the length of parallel sides 22 cm and 12 cm, respectively. The height is 5 cm. Solution: Given: The bases are : a = 22 cm; b = 10 cm; the height is h = ...