If a trapezoid has a top base of 6 and a bottom base of 30 and a height of 15, what is its area?

Asked on by ib1995

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The area of a trapezium with parallel sides of length a and b which are separated by a distance d is given by (1/2)*(a + b)*d.

Here, we have a trapezium with parallel sides of length 6 and 30 and the height which is also the distance separating the parallel sides as 15.

The area of the trapezium is 15*(6 + 30)/2

=> 15*36/2

=> 15*18

=> 270

The required area of the trapezium is 270.

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senseigreen | Middle School Teacher | (Level 1) eNoter

Posted on

For a REGULAR Trapezoid (sides EQUAL) ---> A or B


You need to think of the imaginary lines which come down as the perpendicular from the TOP and hit perpendicular to the bottom.

See them yet?~@

Cutting along those lines, that leaves you with ONE rectangle 6 by 15 [units] and two triangles with height 15 and *___ base.

One of those triangles could be cut loose from the rectangle and rotated so that the hypotenuse [long side] joins to its twin. Now you COULD do the area for two indentical triangles, BUT one rectangle is just as easy.

NOW, add the areas together (6 x 15) + (15 x *___) = Area of Trapezoid

** It is YOUR homework, so YOU figure out what is left and take half that fill in the blank and get the whole answer.

~@ If you have trouble visualizing it, make a template out of graph paper, and cut your lines. Superimpose the trapezoid on the grap paper grid; 6 top, 15 down, base 30 (centered)


>>>> METHOD B-

MENTALLY, (or actually on a grid ) Cut the trapzoid down the center on a perpendicular. Rotate and flip the pieces so that the diagonal sides meet and you SHOULD be able to see an NEW Rectangle from the pieces, and THEN find the area easiest.


++++ IRREGULAR Trapezoid (Unknown/Uneven sides)

You need to take the AREA of two triangles made from the figure cut on a diagonal from one corner to the opposite corner {Trap- ABCD, diagonal from corners A-C}

See it in your head yet?

NOW you should be on easy street AND better understand why there IS a formula for the trapezoid area (which must be paraphrased by this discussion limitations):

1/2(Btop)(H) + 1/2(Base)(H)



OK, so I explained how to MAKE the CLOCK instead of telling you what time it was! Give them all a go, find your favorite explanation and USE it!

ONE problem does not always have ONE solution.

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