A regular pentagon can be divided into 5 congruent triangles. All the triangles have a vertex at the center and edges that go to the vertices of the pentagon.
We know the angles of at the center of each triangle is 72 degrees because a full circle is 360 and we are splitting it into 5 equal parts. 360/5 = 72.
So now we one of the and the height of the triangles (3.4)... To find the length of one of the pentagon's sides, we can use trigonometry. The altitude of the triangles bisects the 72 degree angle to create smaller right triangles. The center angle is 72/2 = 36. Now we can do tan(36) = x/3.4 to find HALF of the side's length. x = 3.4tan(36) = 2.47.. Double that to get 4.94.
Now we can find the area of all 5 triangles. Area is one-half base times height. So 5*(0.5 * 3.4 * 4.94) = 42
So the answer is 42.5 square inches.. The difference comes from rounding differences.