Question

Each length unit on the speedway diagram represents one-tenth of a mile. What is the area of the sector associated with turn A in units of square miles? Use the value 3.142, and round your answer to four decimal places.

Answer 1

We know that 
area of a circle=pi*r²
turn A
r=3 units------> 3*(1/10)----> 0.3 miles
area of a circle=3.142*0.3²-----> 0.28278 miles²

by proportion
0.28278/360°=A/90°------> A=90*0.28278/360------> A=0.0707 miles²

the answer is
0.0707 miles²