What is the answer to this problem

Question

Suppose you cut the home plate (1/2 (8.5 + 17) 8.5) along a dotted line in the middle and rearranged the pieces to form a rectangle what would the dimensions and area be?

Answer 1

This puzzle was a good one, and the trick to it is to calculate the height of the right isosceles triangle atop the rectangular base.

 

The rectangular base has a length of 17", and a width of 8.5". When it is divided, its dimensions will be 8.5" by 8.5"

 

The right isosceles triangle has two legs of 12", and its base is 17". When we calculate the height (from the formula Base = 2(√L2 -H2) ), we get 8.5"

 

So, the new rectangle will have a length of 8.5" and a width of 25.5"

Its area = l x w = 8.5" x 25.5" ≅ 217in²