Area of an odd figure?

[abpp]

Hi. My boy is in 6th grade and has not taken trig or geom yet. He was given this figure to find the area. How can he do it without trig or geom?

 

[MarkFL]

Hello, and welcome to FMH!

Is your son familiar with the formula for the area of a parallelogram? It appears that the shape in question can be deconstructed into two parallelograms. If you extend the line labeled 12 cm all the way to the rightmost edge of the figure, you should see what I mean.

You will have one parallelogram with base 22 cm and height 8 cm and the smaller has base 10 cm and height 1 cm.

 

[Steven G]

...Or you can deconstructed into two parallelograms as follows: Draw a line from the right most point on line marked 12 to the line marked 22 making sure that this line is parallel to the left most line.

I just want to point out that most times you can deconstruct in multiple ways. It is always a good check doing the problem two different ways to see if you get the same answer.

 

[abpp]

Hello, and welcome to FMH!

Is your son familiar with the formula for the area of a parallelogram? It appears that the shape in question can be deconstructed into two parallelograms. If you extend the line labeled 12 cm all the way to the rightmost edge of the figure, you should see what I mean.

You will have one parallelogram with base 22 cm and height 8 cm and the smaller has base 10 cm and height 1 cm.

Perfect! Got it! Thank you!

 

[Harry_the_cat]

Of course, this all assumes that the opposite sides are parallel. Usually this is indicated by arrows or double arrows on the appropriate sides.

 

[firemath]

Or, you could extend the parallelogram to make a 12 x 9 shape, then subtract 12 x 1 from it.