1. **Problem statement:** Calculate the area of the shaded border region around a smaller rectangle inside a larger rectangle. 2. **Given:** - Smaller rectangle dimensions: width $w = 8$ cm, height $h = 6$ cm. - Border width: $b = 1.5$ cm. - Larger rectangle dimensions: width $W = 8 + 2 \times 1.5 = 11$ cm, height $H = 6 + 2 \times 1.5 = 9$ cm. 3. **Formula:** The area of the shaded border region is the difference between the area of the larger rectangle and the smaller rectangle: $$\text{Area}_{\text{border}} = W \times H - w \times h$$ 4. **Calculate areas:** $$W \times H = 11 \times 9 = 99$$ $$w \times h = 8 \times 6 = 48$$ 5. **Calculate shaded area:** $$\text{Area}_{\text{border}} = 99 - 48 = 51$$ 6. **Answer:** The area of the shaded border region is **51 cm$^2$**.