# OHIO STATE

### Area of Ohio

## 44,825 square miles of land/28,688,000 acres of land

You can find the area of Ohio by using

__Law of Cosine__and__Law of Sine__. First "cut" the land into triangles; I used five triangles. Determine the lengths of the sides by using Google Maps. After finding the sides, you can use Law of Cosines to find an angle. Finally you will be able to use Law of Sine to find another angle, then use basic math that a triangles interior angles add up to be 180 degrees, so you can subtract the two angles by 180 to give you the third angle. Continue this process with all five triangles. Finally, you will be able to plug in your sides to the Area formula to a triangle. Do this step to all triangles. Following this step, you should add all the areas to get one large area to cover the Ohio state. In the end, all you will have to do is convert square miles into acres. Then, you have found the area of Ohio!**REMEMBER** THAT ROUNDING MAKES A **BIG** DIFFERENCE, SO IF YOU ARE OFF BY A LITTLE IT IS **OKAY**!

In the photo below, is an example of how to split up the figure into triangles, and these should approximately be the measures of the angles and sides. Again, remember that this is an **approximation**.

If using the example below, the end result should be around 33,138 miles^2.

## Formulas Used

Law of Sines:

Sin(A)/a = Sin(B)/b = Sin(C)/c

Law of Cosines:

a^2 = b^2 + c^2 - 2(a)(b) cos(A)

Area:

A = 1/2 (a)(b) sin(C)