The area of a trapezoid is the number of unit squares that can be fit into it and it is measured in square units (like cm2, m2, in2, etc). For example, if 15 unit squares each of length 1 cm can be fit inside a trapezoid, then its area is 15 cm2. A trapezoid is a type of quadrilateral with one pair of parallel sides (which are known as bases). It means the other pair of sides can be non-parallel (which are known as legs). It is not always possible to draw unit squares and measure the area of a trapezoid. So, let us learn about the formula to find the area of a trapezoid on this page. Show
What is the Area of Trapezoid?The area of a trapezoid is the total space covered by its sides. An interesting point to be noted here is that if we know the length of all the sides we can simply split the trapezoid into smaller polygons like triangles and rectangles, find their area, and add them up to get the area of the trapezoid. However, there is a direct formula that is used to find the area of a trapezoid if we know certain dimensions. Area of Trapezoid FormulaThe area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (a + b) h where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b)
Example: Find the area of a trapezoid whose parallel sides are 32 cm and 12 cm, respectively, and whose height is 5 cm. Solution: The bases are given as, a = 32 cm; b = 12 cm; the height is h = 5 cm. The area of the trapezoid = A = ½ (a + b) h A = ½ (32 + 12) × (5) = ½ (44) × (5) = 110 cm2. Area of Trapezoid without HeightWhen all the sides of the trapezoid are known, and we do not know the height we can find the area of the trapezoid. In this case, we first need to calculate the height of the trapezoid. Let us understand this with the help of an example. Example: Find the area of a trapezoid in which the bases (parallel sides) are given as 6 and 14 units respectively, and the non-parallel sides (legs) are given as, 5 units each. Solution: Let us calculate the area of the trapezoid using the following steps.
How to Derive Area of Trapezoid Formula?We can prove the area of a trapezoid formula by using a triangle here. Taking a trapezoid of bases 'a' and 'b' and height 'h', let us prove the formula.
Thus, we have proved the formula for finding the area of a trapezoid. Area of Trapezoid CalculatorThe area of a trapezoid is the number of unit squares that can fit into it. Area of trapezoid calculator is an online tool that helps to find the area of a trapezoid. If certain parameters such as the value of base or height is available we can directly give the inputs and calculate the area. Try Cuemath's Area of a Trapezoid Calculator and calculate the area of a trapezoid within a few seconds. For more practice check out the area of trapezoid worksheets and solve the problems with the help of the calculator. ☛ Related Articles
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FAQs on Area of TrapezoidThe area of a trapezoid is the number of unit squares that can fit into it. We know that a trapezoid is a four-sided quadrilateral in which one pair of opposite sides are parallel. The area of a trapezoid is calculated with the help of the formula, Area of trapezoid = ½ (a + b) h, where 'a' and 'b' are the bases (parallel sides) and 'h' is the perpendicular height. It is represented in terms of square units. How to Find the Area of a Trapezoid?The area of a trapezoid is found using the formula, A = ½ (a + b) h, where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid. Why is the Area of a Trapezoid ½ (a + b) h?The formula for the area of a trapezoid can be proved easily. Consider a trapezoid of bases 'a' and 'b', and height 'h'. We can cut a triangular-shaped portion from the trapezoid and attach it at the bottom so that the entire trapezoid is rearranged as a triangle. Then the triangle obtained has the base (a + b) and height h. By applying the area of a triangle formula, the area of the trapezoid (or triangle) = ½ (a + b) h. For more information, you can refer to How to Derive Area of Trapezoid Formula? section of this page. How to Find the Missing Base of a Trapezoid if you Know the Area?We know that the area of a trapezoid whose bases are 'a' and 'b' and whose height is 'h' is A = ½ (a + b) h. If one of the bases (say 'a'), height, and area are given, then we will just substitute these values in the above formula and solve it for the missing base (a) as follows: A = ½ (a + b) h Multiplying both sides by 2, 2A = (a + b) h Dividing both sides by h, 2A/h = a + b Subtracting b from both sides, a = (2A/h) - b How to Find the Height of a Trapezoid With the Area and Bases?If the area and the bases of a trapezoid is known, then we can calculate its height using the formula, Area of trapezoid = ½ (a + b) h; where 'a' and 'b' are the bases and 'h' is the height. In other words, we can find the height of the trapezoid by substituting the given values of the area and the two bases. How to Find the Area of an Isosceles Trapezoid Without the Height?If the height of the trapezoid is not given and all its sides are given, then we can divide the trapezoid into two congruent right triangles and a rectangle. Using the Pythagoras theorem in the right-angled triangles, we can calculate the height. After we get the height, we can use the formula, A = ½ (a + b) h, to get the area of the trapezoid. What is the Formula for Area of Trapezoid?The formula that is used to find the area of a trapezoid is expressed as, Area of trapezoid = ½ (a + b) h; where a' and 'b' are the bases (parallel sides) and 'h' is the height of the trapezoid. |