Look at the trapezoid ABCD shown below.

Using complete sentences, explain how the formula for the area of trapezoid ABCD is derived.

Question

Look at the trapezoid ABCD shown below. 

 

Using complete sentences, explain how the formula for the area of trapezoid ABCD is derived.

anonymous · Answer

attachment

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

Imagine you rotated the given trapezoid 180 degrees and you glued together one of the nonparallel sides like you see in the attached image

jim_thompson5910 · Answer

What is the base of that parallelogram I just created?

jim_thompson5910 · Answer

Any ideas?

anonymous · Answer

no:((

jim_thompson5910 · Answer

It might be hard to see, but do you see the upside down b2?

jim_thompson5910 · Answer

On the right (bottom) base?

jim_thompson5910 · Answer

Basically the base of the parallelogram is b1 + b2

jim_thompson5910 · Answer

This is because we've glued the two trapezoids, so the two bases "glue" into one longer base

jim_thompson5910 · Answer

What is the height of this parallelogram?

jim_thompson5910 · Answer

You'd agree that it's just h right?

anonymous · Answer

yes

jim_thompson5910 · Answer

So the area of the parallelogram is...

Area = Base times Height


A = (b1+b2)*h

A = h(b1+b2)

jim_thompson5910 · Answer

but...this isn't the area of the trapezoid

In fact, the trapezoid is exactly half this (since we cloned the trapezoid, rotated and glued to get the parallelogram)

So 

Area of trapezoid = (Area of parallelogram)/2

Area of trapezoid = h(b1+b2)/2

jim_thompson5910 · Answer

which is exactly the formula we're used to

jim_thompson5910 · Answer

hope that made sense