what is a trapezoid how to find the area of a trapezoid

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A trapezoid, also known as a trapezium, is a 4-sided shape with 2 parallel bases that are unlike lengths. The formula for the area of a trapezoid is A = ½(b_one+b₂)h, where b₁ and b_ii are the lengths of the bases and h is the height. If y'all merely know the side lengths of a regular trapezoid, yous can break the trapezoid into uncomplicated shapes to notice the height and terminate your calculation. When yous're finished, merely label your units!

1. one

   Add together the lengths of the bases. The bases are the ii sides of the trapezoid that are parallel with one another. If you aren't given the values for the base of operations lengths, and so utilise a ruler to measure each one. Add the ii lengths together so you lot have i value.^[i]

   • For case, if yous find that the top base of operations (b₁) is viii cm and the bottom base of operations (b₂) is 13 cm, the full length of the bases is 21 (eight cm + 13 cm = 21 cm, which reflects the "b = b₁ + b₂" office of the equation).

2. ii

   Measure out the meridian of the trapezoid. The height of the trapezoid is the distance between the parallel bases. Draw a line betwixt the bases, and use a ruler or other measuring device to find the distance. Write the height down so you don't forget it subsequently in your calculation.^[2]

   • The length of the angled sides, or the legs of the trapezoid, is not the same equally the height. The leg length is just the same every bit the tiptop if the leg is perpendicular to the bases.

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3. 3

   Multiply the full base of operations length and pinnacle together. Take the sum of the base of operations lengths you found (b) and the height (h) and multiply them together. Write the product in the appropriate square units for your trouble.^[iii]

   • In this example, 21 cm x seven cm = 147 cm² which reflects the "(b)h" part of the equation.

4. 4

   Multiply the product by ½ to find the area of the trapezoid. Y'all can either multiply the production by ½ or divide the production by ii to get the final area of the trapezoid since the result will exist the same. Make sure you characterization your terminal answer in square units.^[4]

   • For this case, 147 cm² / 2 = 73.five cm², which is the area (A).

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1. 1

   Pause the trapezoid into 1 rectangle and 2 right triangles. Draw straight lines down from the corners of the top base of operations so they intersect and course 90-degree angles with the lesser base. The inside of the trapezoid will have 1 rectangle in the middle and ii triangles on either side that are the same size and take ninety-caste angles. Cartoon the shapes helps you lot visualize the area meliorate and helps you lot find the height of the trapezoid.^[5]

   • This method only works for regular trapezoids.

2. two

   Find the length of one of the triangle'due south bases. Decrease the length of the peak base from the length of the bottom base to notice the amount that's left over. Separate the corporeality by 2 to find the length of the triangle's base. Y'all should now take the length of the base of operations and the hypotenuse of the triangle.^{[half dozen]}

   • For case, if the top base of operations (b₁) is vi cm and the bottom base (b₂) is 12 cm, then the base of the triangle is 3 cm (because b = (b_two - b₁)/two and (12 cm - half-dozen cm)/ii = half dozen cm which can be simplified to 6 cm/two = 3 cm).

3. iii

   Use the Pythagorean theorem to detect the peak of the trapezoid. Plug the values for the length of the base of operations and the hypotenuse, or the longest side of the triangle, into A² + B² = C², where A is the base and C is the hypotenuse. Solve the equation for B to discover the height of the trapezoid. If the length of the base you establish is three cm and the length of the hypotenuse is five cm, and so in this example:^[vii]

   • Fill up in the variables: (3 cm)² + B² = (5 cm)ⁱⁱ
   • Simplify the squares: 9 cm +B² = 25 cm
   • Subtract 9 cm from each side: B² = sixteen cm
   • Take the square root of each side: B = 4 cm

   Tip: If y'all don't have a perfect square in your equation, and so simplify it every bit much as possible and go out a value with a square root. For example, √32 = √(16)(ii) = 4√2.

4. iv

   Plug the base of operations lengths and summit into the area formula and simplify it. Put the base lengths and the height into the formula A = ½(b_i +b₂)h to find the area of the trapezoid. Simplify the number equally much every bit you lot can and label information technology with square units.^[eight]

   • Write the formula: A = ½(b₁+b₂)h
   • Fill in the variables: A = ½(half dozen cm +12 cm)(4 cm)
   • Simplify the terms: A = ½(xviii cm)(4 cm)
   • Multiply the numbers together: A = 36 cm^two.

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Add New Question

• Question

  How do I notice the area if given only the shorter base of operations and height?

  

  Yous have to know the lengths of both bases (as well every bit the meridian) in club to find the area.

• Question

  Why do I dissever by two?

  

  You're really finding the boilerplate of the two bases kickoff (by adding their lengths and dividing by ii) and then multiplying by the height.

• Question

  Will this formula piece of work with every trapezoid?

  

  Yes. Even though not all trapezoids are the same size, it will nevertheless work if you lot plug the numbers in correctly.

• Question

  How do I check an answer to the area of a trapezoid?

  

  Employ the opposite formula: If the Area of a trapezoid is (B1+B2)*h/2, and so to check your reply endeavour to find one of the other values. For example, try to find h (height); h = A*2/(B1+B2). If the answer you've only calculated is the same every bit the value that the problem gives you lot for h (and assuming your calculations are exact), so the Area is correct. This procedure also works for B1 and B2, B1 = [(A*2)-B2]/h, B2 = [(A*2)-B1]/h.

• Question

  How practise I discover the base of a parallelogram when elevation and area are given?

  

  Split up the area by the height.

• Question

  What is the circumference of a circle?

  

  The ratio between the circumference of a circle and its diameter is always the same for any circle, no matter how large or small the circle is, and it is equal to approximately 3.1415. So, to calculate the circumference of the circumvolve, but multiply its diameter with 3.1415.

• Question

  How practice I observe the top of the trapezoid when but the bases are given?

  

  Yous would besides have to know the area. Divide the area past one-half the sum of the bases.

• Question

  How do I know if it's a trapezoid or not?

  

  A effigy is a trapezoid if information technology has iv sides, ii -- and only 2 -- of which are parallel to each other. The parallel sides must exist of diff length.

• Question

  Volition information technology still work if I do this: if B1 > B2 : A = (B1 - B2) / ii + B2) x H; if B2 > B1 : A = (B2 - B1) / two + B1) 10 H?

  

  Yeah, that works.

• Question

  How practise I find the height of a trapezoid when the area and the bases are given?

  

  Add the ii bases together and divide by two. And then accept that number and divide it into the area. That volition give you lot the height.

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• If you know the median of the trapezoid, which is a line that runs parallel to the bases through the middle of the shape, and so multiply information technology by the superlative to go the area.^[9]

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Commodity Summary X

To detect the expanse of a trapezoid, commencement by adding together the length of the bases, which are the two sides of the trapezoid that are parallel with each other. And so, multiply that number by the height of the trapezoid. Finish by dividing the production by 2 to find the area. For example, if one of the trapezoid'south bases is 8 inches long and the other one is 12 inches long, first you'd add those together and get twenty inches. Then, if the trapezoid's meridian was 10 inches, you'd add that to 20 and become 30. Just divide 30 by two to get 15, which is the area of the trapezoid. To acquire how to summate the area of a trapezoid if y'all only know the sides, gyre down!

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Source: https://www.wikihow.com/Calculate-the-Area-of-a-Trapezoid

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