Question

how to solve 34×17 using an area model

Answer 1

34 x 17=578 is the same as 34 x 10 =340
+ 34 x 7= 238
34 x 10=340 is the same as 30 x 10=300 + 4 x 10=40
34 x 7 =238 is the same as 30 x 7=210 
+4 x 7=28
the areas are: 300 + 40 + 210 + 28=578

Answer 2

The main idea behind area model is to crack multiplication of 2 larger numbers in sum of several easier to calculate multiplications of smaller numbers. Each multiplication of those smaller numbers is represented by part of the area in the picture.
So, we can write down number 34 as sum of 30 and 4 and number 17 as sum of 10 and 7.

Going further we can write down:
34*17=(30+4)*(10*7)=30*10+30*7+4*10+4*7=578