Questions: What are the perimeter and area of the shaded region? All angles are 90 degrees. The perimeter of the shaded region mi. The area shaded region is mi^2.

Solution Steps

The shaded region is a composite shape made up of rectangles. We need to break it down into simpler parts to find the perimeter and area.

The shaded region can be divided into two rectangles:

• The larger rectangle has dimensions 33 mi by 14 mi.
• The smaller rectangle that is subtracted from the larger one has dimensions 21 mi by 6 mi.

Area of the larger rectangle: \[ \text{Area} = 33 \, \text{mi} \times 14 \, \text{mi} = 462 \, \text{mi}^2 \]

Area of the smaller rectangle: \[ \text{Area} = 21 \, \text{mi} \times 6 \, \text{mi} = 126 \, \text{mi}^2 \]

Area of the shaded region: \[ \text{Area} = 462 \, \text{mi}^2 - 126 \, \text{mi}^2 = 336 \, \text{mi}^2 \]

To find the perimeter, we need to add up the lengths of all the outer sides of the shaded region.

The perimeter includes:

• Top side: 33 mi
• Bottom side: 33 mi
• Left vertical side: 14 mi
• Right vertical side: 14 mi
• Two inner vertical sides: 6 mi each (total 12 mi)
• Two inner horizontal sides: 21 mi each (total 42 mi)

Total perimeter: \[ \text{Perimeter} = 33 \, \text{mi} + 33 \, \text{mi} + 14 \, \text{mi} + 14 \, \text{mi} + 6 \, \text{mi} + 6 \, \text{mi} + 21 \, \text{mi} + 21 \, \text{mi} = 148 \, \text{mi} \]

Final Answer