Q&A for How to Calculate the Area of a Trapezoid

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How do I find the area if given only the shorter base and height?

Donagan

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You have to know the lengths of both bases (as well as the height) in order to find the area.

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Question

Why do I divide by two?

Donagan

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You're actually finding the average of the two bases first (by adding their lengths and dividing by two) and then multiplying by the height.

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Will this formula work with every trapezoid?

Community Answer

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

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

Community Answer

Use the reverse formula: If the Area of a trapezoid is (B1+B2)*h/2, then to check your answer attempt to find one of the other values. For example, attempt to find h (height); h = A*2/(B1+B2). If the answer you've just calculated is the same as the value that the problem gives you for h (and assuming your calculations are exact), then the Area is correct. This procedure also works for B1 and B2, B1 = [(A*2)-B2]/h, B2 = [(A*2)-B1]/h.

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How do I find the base of a parallelogram when height and area are given?

Donagan

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Divide the area by the height.

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What is the circumference of a circle?

Community Answer

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 circle, simply multiply its diameter with 3.1415.

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Question

How do I find the height of the trapezoid when only the bases are given?

Donagan

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You would also have to know the area. Divide the area by half the sum of the bases.

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

Donagan

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A figure is a trapezoid if it has four sides, two -- and only two -- of which are parallel to each other. The parallel sides must be of unequal length.

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Question

Will it still work if I do this: if B1 > B2 : A = (B1 - B2) / 2 + B2) x H; if B2 > B1 : A = (B2 - B1) / 2 + B1) x H?

Donagan

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Yes, that works.

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

Community Answer

Add the two bases together and divide by two. Then take that number and divide it into the area. That will give you the height.

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The area of a trapezoid is 66 square feet. If its two bases are 8 and 14 feet, how do I find its height with |A=(1)/(2)(b+B)h|?

Donagan

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Reworking the formula, h=(2A) ÷ (b+B).

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What if the trapezoid has 2 right angles?

Donagan

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That's called a right trapezoid.

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If there are two bases, 5 cm and 17 cm, and the equal length of side of isoscale trapezium is 10 cm, then how do I calculate area?

Donagan

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To make sense of this, you should draw the trapezoid, letting the upper base be 5 and the lower base be 17. Then drop two heights (h) from the upper-left and upper-right corners to the lower base. Then do the following: Subtract the shorter base from the longer base, and divide by 2. (This works only with an isosceles trapezoid.) That gives you 6, which is the distance from either lower corner to the point where the height lines meet the lower base. Using the Pythagorean Theorem, 6² + h² = 10². Therefore, h² = 10² - 6² = 64. So h = 8. Use the formula above to find the area.

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What if there is more than one height?

Donagan

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A trapezoid is defined as having two parallel bases, so there would be only one height.

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If I have an isosceles trapezoid, what is the relationship of the top base to the bottom base?

Donagan

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Other than the fact that they are parallel, there is no specific relationship.

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How do I know if I got it right?

Community Answer

You can solve the problem multiple times and if you continue to get the same answer, chances are that you got it correct.

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Question

Where do I find the width?

Community Answer

Measure the width at the bottom and top of the trapezoid.

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How do I estimate the area of a trapezoid?

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You round the bases and height to the nearest whole number and then you do the same process.

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Question

H stands for height, B stands for base, but what does A stand for?

Community Answer

A stands for area, which is what you are trying to find.

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Question

What does the '1/2' in the formula for the area of a trapezoid mean?

Donagan

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The '1/2' is applied to the sum of the bases to calculate their average length. This average length is then multiplied by the height to determine the area of the trapezoid.

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How can I understand the formula for calculating the area of a trapezoid?

Donagan

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To calculate the area of a trapezoid, you multiply its height by the average length of its two parallel bases. You determine the average length by adding the lengths of the two bases together and then dividing that sum by two.

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How can I calculate the area of a trapezoid if I don't know the length of its bases?

Donagan

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You cannot calculate the area of a trapezoid unless you know the length of both bases and the height.

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Why can't I learn my times tables yet even though I am 13?

Donagan

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You can learn them. It's just a matter of hard work and memorization. Flash cards are a good tool for that kind of learning. You can buy the cards or make them yourself.

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The trapezoid area is 52, its altitude is 8, and its long base is 10.

Donagan

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Assuming you want the short base, let x equal the length of the short base. Now 52 / 8 = 6.5. 6.5 = (10 + x) / 2. Then (10 + x) = 13, and x = 3.

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If the trapezoid isn't an isosceles (it doesn't have two right triangles at the end or the non-parallel sides aren't equal), how do I calculate the area?

Donagan

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Use the area formula given in the article above. The trapezoid does not have to be isosceles for the formula to work.

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What if I have a trapezoid that has vertical parallels lines and 4 values? Does it still work?

Donagan

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What you're describing sounds like a rectangle. It's unclear what you mean by "4 values." The formula for the area of a trapezoid does work for a rectangle.

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So, either the top or bottom can be the base?

Donagan

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Yes. The "bottom" of a trapezoid is usually called "the base," but actually each of a trapezoid's parallel sides is considered a base (b1 and b2 in the area formula).

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The difference of 2 base is 12cm- and the minor base is 4/5 of major base. What is the area of trapezoid if the height is 36cm?

Donagan

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Let "x" be the major base. Then 4x/5 is the minor base. So x - (4x/5) = (5x/5) - (4x/5) = x/5 = 12, and x = 60. Then the minor base is 60 - 12 = 48. Half the sum of the bases is (60 + 48) / 2 = 54. The area is (54)(36) = 1944 sq cm.

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Not a question but a comment. The example with 1/2(18) x 4 is incorrect because it only divides the addition of the bases in half. The correct way would be to do 18 x 4 first, then divide by 2.

Donagan

Top Answerer

No. The text above is correct. The formula for a trapezoid's area is "height multiplied by half the sum of the bases" (in other words, "height times median.")

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What about finding the perimeter?

Donagan

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See Find the Perimeter of a Trapezoid .

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