A trapezoid is a 4-sided flat shape with one pair of parallel sides called its bases. The height (also called altitude) of a trapezoid is perpendicular to its bases. The other two non-parallel sides are called legs. Examples of trapezoid-shaped objects are flowerpots, handbags, pails, and other architectural things. Show
See the illustration of a trapezoid below.  How to Find the Area of a TrapezoidThe area of a 2-dimensional shape refers to the total amount of space enclosed within that shape. It is measured in cubic units, such as m2, cm2, km2, and in2. Make sure all units are the same before you compute. Related Reading: Area of a Circle – Formula & Examples To find the area of a trapezoid, multiply the average of the trapezoid’s two bases (parallel sides) and its height, as expressed in this formula: A = (a + b) / 2 • h Example #1: Finding the Area of a Trapezoid when Given Measurements with the Same UnitsFind the area of a trapezoid with the following measurements: Solution to Example #1:Step 1. Write the given figures: a = 10cm, b = 8cm, h = 6cm. Therefore, the area of the trapezoid is 54cm2. Example #2: Finding the Area of a Trapezoid when Given Measurements with Different UnitsFind the area of the trapezoid below. Solution to Example #2:Step 1. Write the given measurements: a = 5yd, b =126in, h = 4yd. Therefore, the area of the trapezoid is 17yd2. Example #3: Finding the Base of a TrapezoidFind the other base of a trapezoid that has an area of 71.5cm2, height of 6.5cm, and base of 9cm. Solution to Example #3:Step 1. Write the formula for the area of a trapezoid: A = (a + b) / 2 • h OR A = (a + b)h / 2. Therefore, the length of the other base is 13cm. Checking the Solution to Example #3:Plug the measurements into the formula for the area of trapezoid. Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the area of a trapezoid. 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.
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: A = ½ (a + b) h Here (A) is the area of a trapezoid. ‘a’ and ‘b’ are the parallel sides of the trapezoid ‘h’ is the height, i.e., the perpendicular distance between the parallel sides. Area of Trapezoid ExampleHere 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 = 5 cm. The area of the trapezoid = A = ½ (a + b) h A = ½ (22 + 10) × (5) A = ½ (32) × (5) A = ½ × 160 A = 80 cm2Example 2: Find the area of a trapezoid whose parallel sides are given as 10cm and 16cm, respectively, and the non-parallel sides are 5cm each. Solution: Since in this question, we don’t have the height of the trapezium, we will follow the following steps to calculate the area of the trapezoid. Given: a =10 cm; b =16 cm; non-parallel sides = 5 cm each Step 1: To find the height of the trapezoid, we will first draw the height of the trapezoid on both sides. Now we can see that the trapezoid consists of a rectangle ABQP and 2 right-angled triangles, APD and BQC. Step 2: Now, we have to find the length of DP and QC. Since ABQP is a rectangle, AB = PQ DC = 16 cm (Given) So, PQ = AB We can find the combined length of DP + QC as follows DC – PQ = 16 – 10 = 6 cmSo, DP + QC = 6 6 ÷ 2 = DP = QC 3 cm = DP = QC Step 3: AP = BQ (opposite and equal sides of a rectangle) AD = BC = 5 cm (Given) So, we can calculate the height AP and BQ using Pythagoras theorem. In the right-angled triangle ADP AP = √(AD2 – DP2) AP = √(52 – 32) AP = √(25 – 9) = √16 = 4 cm Since ABQP is a rectangle, the opposite sides will be equal. So, AP = BQ = 4 cm. Step 4: Now we know all the dimensions of the trapezoid. We can calculate the area using the formula. Area of a trapezoid = ½ (a + b) h; where h = 4 cm, a =10 cm b = 16 cm On substituting values we get: Area = ½ (10 + 16) × 4 Area = ½ × 26 × 4 Area = 52 cm2 We can calculate by adding area of the rectangle and two triangles Area of trapezoid = Area of ABPQ + Area of ADP + Area of BQC Area of trapezoid = (l × b) + 2( ab/2) Area of trapezoid = (10 × 4) + 2(3 ×4/2) A = 40 + 12 A = 52 cm2 Trapezoidal PrismA trapezoidal prism is a 3D figure made up of two congruent trapezoids that are connected by four rectangles. The trapezoids are on the top and the bottom. Thus, they form the base for prisms and have polygons that form their bases. The four rectangles form the lateral faces of the trapezoid prism. So, a trapezoidal prism consists of-
Surface Area of a Trapezoidal PrismThe area of a trapezoidal prism is the sum of the surfaces of the prism. This area equals the areas of all of the faces of the trapezoid prism. Since a trapezoidal prism has two trapezoidal faces and four rectangular faces, a sum of their areas will give the surface area of the prism. However, there is a simple and direct formula for calculating the surface area of a trapezoid prism. The formula is: Surface Area of a Trapezoidal Prism = h (b + d) + l (a + b + c + d) square units. Here, h = height b and d are the lengths of the base a + b + c + d is the perimeter l is the lateral surface area of a trapezoidal prism Derivation of Surface Area of a Trapezoidal PrismThe base of a trapezoidal prism is trapezoid in shape. Here, b and d are parallel sides of the trapezoid H = distance between the parallel sides l = length of the trapezoidal prism So, the total surface area of a trapezoidal prism (TSA) = 2 × areas of base + lateral surface area ————- (1) Area of a trapezoid = ½ (base 1 + base 2) height So, area of trapezoidal base = h (b + d)/2 ——————— (2) The lateral area of a trapezoidal prism (LSA) = sum of the areas of each rectangular surface So, LSA = (a × l) + (b × l) + (c × l) + (d × l) ——————- (3) On substituting the values from equation (2) and equation (3) in equation 1 i.e., TSA formula, we get: (TSA) = 2 × h (b + d)/2 + (a × l) + (b × l) + (c × l) + (d × l) TSA = h (b + d) + [(a × l) + (b × l) + (c × l) + (d × l)] Total surface area of a trapezoidal prism = h (b + d) + l (a + b + c + d) Thus, TSA of a trapezoidal prism = h (b + d) + l ( a + b + c + d) unit square How to Find the Surface Area of a Trapezoidal Prism? Here are the steps on how to find the surface area of a trapezoidal prism. Step 1: Spot the four sides of the trapezium – a, b, c, and d. These represent the widths of the four rectangles. The addition of these 4 values will give the perimeter P. Step 2: Spot the length h of the prism. Step 3: Find the lateral area of a trapezoidal prism. Step 4: Identify b1, b2 and h of the trapezoid. Now, find the base area B using the formula, (b1 + b2) h/2 Step 5: Lastly, put the values in the formula = 2B + Lateral Surface Area to calculate the total surface area of the trapezoidal prism. Consider the following example of the surface area of a trapezoidal prism for a clearer understanding. Example 1: Find the total surface area of an isosceles trapezoidal prism that has parallel edges of the base 8 cm and 12 cm. The legs of the base are 5 cm each, the altitude of the base is 4 cm and the height of the prism is 10 cm.Solution: The perimeter of the base = sum of the length of the sides. p=8+5+12+5=30 cm Given that the base is an isosceles trapezoid, therefore, the area = 1/2h(b1+b2) Area of base =1/2(4)(8+12)=40 cm2 T.S.A.= ph+2B T.S.A = 30(10)+2(40) T.S.A =300+80 =380 cm2 TESTIMONIALSAyaan always had a special interest in Math. His knowledge and problem solving skills in math has been improving after enrolling in Turito's One-on-One onlineTutoring. The tutors are very co-operative and the valuable tips given by them made his learning more enjoyable.They were also very interactive and my son is able to communicate better than ever before. The best thing about Turito’s one-on-one tutoring is the flexible timings and the tutors are at our reach anytime, anywhere. This actually made my son’s learning seamless and saved a lot of time. Parent: Dr.Sadaf asad | Subject : Math I witnessed a significant improvement in the English language skills of my son Trijal, after enrolling in Turito’s one-on-one tutoring. The sessions were undoubtedly interesting. Though Trijal is shy by nature, now he is able to interact smoothly because the tutors established a friendly rappo with him. Parent: Kamal Narang | Subject : English My daughter, Karmanpreet’s English grammar, Reading and spelling skills have tremendously improved after enrolling in Turito's One-On-One Tutoring. Their services are flexible, and the tutors are very co-operative. She looks forward to these sessions as they include fun activities and make learning quite enjoyable and stress-free. Parent: Gurpreeth Sandhu | Subject : English Previous Next SIGNUP FOR AFREE SESSION
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The height of the parallelogram is the same as the height of the trapezoid, but its base is the sum of the two bases of the trapezoid. So the parallelogram's area is height × (base1 + base2). But that area is two trapezoids, so we need to cut it in half to get the area of the trapezoid.
How do you find the area of a trapezoid without formula?A trapezoid is a quadrilateral geometric shape characterized as having a two parallel and two nonparallel sides. The area of a trapezoid can be calculated as the product of the height and the average of the two parallel sides, also known as bases.
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How do you find area of a trapezoid
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