One of the bases of a trapezoid has length 10, and the height of the trapezoid is 4. If the area of the trapezoid is 48, then how long is the other base of the trapezoid?

Guest Oct 18, 2020

#1**0 **

The area of a trapezoid is: (base1+base2)/2*height=area

So, let's plug in the values and put in the unknown value as a variable :)

(x=the unknown base length)

(10+x)/2 * 4=48

20+2x=48

2x=28

x=14

So, the other base would have a length of 14 units.

Please correct me if I'm wrong :)

CalTheGreat Oct 18, 2020

#2**+1 **

Hi Cal,

I always balk when I see the word Trapezoid.

In Australia we call the Trapeziums.

Your answer is excellent. :)

Melody
Oct 18, 2020

#3**+1 **

*Trapezoid* and *Trapezium *are in use in both**American (US) and European English;** __however, the formal meanings are____ reversed.__

*Geometry*. ** Trapezoid** (Greek)

- a quadrilateral plane figure having two parallel and two nonparallel sides.
*British*. trapezium (def. 1b).

Source: https://www.dictionary.com/browse/trapezoid

*Geometry*. ** Trapezium** (Latain)

1. (in Euclidean geometry) any rectilinear quadrilateral plane figure not a parallelogram.

2. a quadrilateral plane figure of which no two sides are parallel.

* 3. British*. trapezoid (def. 1a).

Source: https://www.dictionary.com/browse/trapezium

Wikipedia offers a more detailed history for the etymology of these words

https://en.wikipedia.org/wiki/Trapezoid

GA

--. .-

GingerAle
Oct 18, 2020

#5**0 **

Melody + Ginger

Well, I learned something new today!!

Thanks for the interesting fact, @GingerAle

And thanks for the compliment too! (Melody)

CalTheGreat
Oct 18, 2020

#4**0 **

Hi Ginger,

It is very nice to see you.

So in the USA a kite would qualify as a Trapezium. In Britain it would qualify as a Trapezoid.

And here I would only ever have called it a kite or, more generally, a quadrilateral.

Before I started using this forum I had never seen the work Trapezoid used.

Oblong is another strange word that I see sometimes. I think it just is a rectangle.

Cheap tablecloths from China (in our shops) are often referred to as oblong in shape.

Melody Oct 18, 2020

#6**+2 **

Hi Melody,

*So in the USA a kite would qualify as a Trapezium.*

. I probably wasn’t paying attention in class, but I don’t remember my geometry teacher referring to a kite to as a trapezium; though I suppose it may be a special case, where the pairs of equidistant lines are always adjacent. This is similar in scheme to how a square is also a rhombus, rectangle, and parallelogram. LOL. I have sometimes heard of a *kite* referred to as a *diamond *shape.

Oblong is a word I’ve heard since childhood. I think of it as an elongated oval or an ellipsoid blended with a rectangle; or a rectangle with the longer sides parallel, or nearly so, with continuously rounded corners for the width. In some old texts, I’ve seen the word oblong used to mean rectangle.

Oval comes from the Latin *Ovum* –for egg, so it is egg-shaped. Specifically the shape refers to the eggs of the *Gallus domesticus* (domestic chicken), which has been familiar to most people for centuries.

Most of my early education on shapes was from art classes. My high school Latin teacher also spent many classroom hours teaching the nuances of shapes in second and third-year Latin. There are many Latin words describing shapes, and most were introduced in very early Latin dialects; the influence of the Greek is notable in many of these words.

Later, I learned that shapes that are graphical curves have both precise and general mathematical functions that produce them, such as parabolas, catenaries, ellipsis, and hyperbolas. Because of the mathematical functions, there is little ambiguity about the shape; for example, how a catenary may be confused for a parabola.

...So much to learn and so little time to learn it....

------------------------------------

*It is very nice to see you*.

Thank you.

When I open web2.0calc’s forum pages and see posts by Melody, Alan, and ...ah ...ah ..., whoever the third answerer is now, I know that at least one part of the (virtual) world is functioning within normal parameters, even if the forum’s OS sometimes does not.

GA

--. .-

GingerAle
Oct 20, 2020

#7**+1 **

**Oh, gorblimey!** *Pawsing* to read Omi’s post definitely rings a bell and it’s doggone funny....

I figured out who the third answerer is: ElectricPawlow.

Hmmm... I’m suddenly hungry for a banana...

...I think this conditioned response comes from Lancelot Link’s phones with the *Banana- Pealing*

GA

--. .-

GingerAle
Oct 20, 2020