Area of a Trapezoid ( different / with a twist ) ?

[Meep]

Hi , I'm in Grade 7 and we're currently learning about the 5 different ways to find the area of a Trapezoid.

So we got this question about "Alpha" & "Beta" who changed their rectangular lots into trapezoids.
The question wants to know if the area of their lots changed - do they more space or less?

( all measurements in mm )

So as Rectangles ( they had equal lots ) ; <--- The area will be bxh. So A = 1050mm
Length - 35mm
Width - 30mm

Now we haven't learnt how to calculate the area of a trapezoid with a formula, so the question wants to know if we can find the area of the trapezoid knowing SUM of the lengths of the parallel lines & the distance between them.

So the trapezoids :
Sum of the lenghts of the parallel sides : 70mm
Distance between the parallel sides : 30 mm

I thought I could just say that the area is also 1050 and be done, but there's this question asking how to find the area knowing this info.
( Question Below in Bold )

Now that I've given the info, here's the actual question :

Explain how to calculate the area of a trapezoid containing a right angle, given the sum of it lengths of its parallel sides & distance between them.

I'M SOOO CONFUSED RIGHT NOW!! PLEASE HELP, I'M USUALLY PRETTY GOOD WITH MATH, BUT THIS MESSED ME UP D:
IF THERE IS ANY MISSING INFO THAT YOU NEED TO KNOW PLEASE TELL ME & I'LL FILL YOU IN. ~

 

[soroban]

Hello, Meep!

Explain how to calculate the area of a trapezoid containing a right angle,
given the sum of it lengths of its parallel sides & distance between them.

We are given this trapezoid.

      : - a - :
      *-------*
      |        \
    h |         \
      |          \
      *-----------*
      : - - b - - :

We know the sum \(\displaystyle a+b\) and height \(\displaystyle h.\)


Make a copy of the trapezoid, invert it,
. . and append it to the right end.

      : - a - : - - b - - :
      *-------*-----------*
      |        \::::::::::|
    h |         \:::::::::|
      |          \::::::::|
      *-----------*-------*
      : - - b - - : - a - :

We have a rectangle with base \(\displaystyle a+b\) and height \(\displaystyle h.\)
Its area is: .\(\displaystyle h(a+b).\)

Since the area of the rectangle is twice that of the trapezoid,
. . the area of the trapezoid is: .\(\displaystyle A \:=\:\tfrac{1}{2}h(a+b).\)