Part A: What is the shortest distance between the gymnasium and the library? Round your answer to the nearest tenth of a kilometer. Part B: Gabe walks the shortest distance from his house to the gymnasium, then the shortest distance to the library. What is the total distance Gabe walked?

4.5 km

10.3 km

Step-by-step explanation:

The shortest distance from gymnasium to library:

Each square box representing 1 unit

1unit = 1 km

A.)

Distance, d ;

Using Pythagoras :

d = sqrt(2² + 4²)

d = sqrt(4 + 16)

d = sqrt(20)

d = 4.47

d = 4.50 (nearest tenth)

Shortest Distance from gymnasium to library

B.)

shortest distance from his house to the gymnasium, then the shortest distance to the library

House to gymnasium (d1) :

d1 = sqrt(3² + 5²)

d1 = sqrt(9 + 25)

d1 = sqrt(34)

d1 = 5.83

Gymnasium to Library (d2) :

d2 = sqrt(2² + 4²)

d2 = sqrt(4 + 16)

d2 = sqrt(20)

d2 = 4.47

Total distance = (d1 + d2) = (5.83 + 4.47) = 10.3km

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2