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In this lesson, we will learn about the area of a trapezoid.

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First, let's consider this trapezoid with the height ‘h’, and two parallel sides, ‘a’ and ‘b’ respectively.

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Now, to find the area of a trapezoid A, first we add ‘a' and 'b' together, and divide the added numbers with 2.

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This gives (a+b)/2. Next, we multiply (a+b)/2, with the height of the trapezoid, ‘h’.

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Hence, now we have the formula for the area of a trapezoid, A = ((a+b)/2)h.

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Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

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We will see more explanations on this, in the upcoming example.

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Now, let's see some examples on using this formula.

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Find the area of this trapezoid when its height is 4cm, and the parallel sides are 5cm, and 9cm respectively.

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First, we start with the formula for the area of a trapezoid, A = ((a+b)/2)h.

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Since the shorter parallel side is given as 5cm, we can substitute ‘a’ with 5.

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Similarly, since the longer parallel side is given as 9cm, we can substitute 'b' with 9.

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Next, we can simplify by adding 5 with 9. This gives 14.


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14 divided by 2, gives 7.

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Now, since the height is given as 4cm, we can substitute 'h' with 4.

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Multiplying 7 with 4, gives 28.

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Note that, this number has no meaning unless we include the unit for it.

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Since the sides of the trapezoid are in centimeter, the unit for the area will be in square

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Hence, the area of this trapezoid is 28 square centimeter.

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Next example, given that the area of this trapezoid is 9 square feet, and it parallel sides are 2ft, and 4ft respectively. Find its height.

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Again, we start with the formula for the area of a trapezoid, A = ((a+b)/2)h.

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Now, since the area, and the 2 parallel sides are given, we can find the height by solving this equation for h. Here's how.

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Since the area is given as 9 square feet, we can substitute 'A' with 9,

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Similarly, since the shorter parallel side is given as 2cm, we can substitute 'a' with 2.

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Again, since the longer parallel side is given as 4cm, we can substitute 'b' with 4.

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We can simplify this equation, by adding 2 with 4. This gives 6. 6 divided by 2, gives 3.

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(3)h is the same as 3h.

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Now, we have 3h equals to 9.

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Let's rewrite this equation so that it will look neater.

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To find 'h' we need to remove 3. We can do so by dividing both sides of the equation with 3.

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By doing so, we have, ’h’ equals to 9 over 3.

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9 divides by 3, gives 3.

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Now, this number is meaningless unless we include the unit for it.

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Since the parallel sides are given in feet, the height of the trapezoid will be in feet.

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Therefore, the height of this trapezoid is 3ft.

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That is all for this lesson. Try out the practice question to further your understanding.