What is the area of the Earth near both sides of the equator called?

The equator divides the Earth into two hemispheres i.e., the northern hemisphere and the southern hemisphere. 

The regions near the equator in both hemispheres are known as the tropics. Tropics are also called torrid zones. The tropic lying in the northern hemisphere is called the Tropic of Cancer whereas, the tropic in the southern hemisphere is called the Tropic of Capricorn.

Thus, the area of the Earth near both sides of the equator is called the tropics.