Comprehensive Measurement and Circle Geometry Review

Problem 16: Rectangular Prism Surface Area (km)
- Dimensions: $20\,km, 20\,km, 4\,km$ .
- Formula: $SA = 2(lw + lh + wh)$ .
- Calculation: $SA = 2[(20\times 20) + (20\times 4) + (20\times 4)] = 2[400 + 80 + 80] = 1120\,km^2$ .
- Result: $1120\,km^2$ .
Problem 17: Rectangular Prism Surface Area (cm)
- Dimensions: $14\,cm, 4\,cm, 2\,cm$ .
- Calculation: $SA = 2[(14\times 4) + (14\times 2) + (4\times 2)] = 2[56 + 28 + 8] = 2[92] = 184\,cm^2$ .
- Result: $184\,cm^2$ .
Problem 18: Triangular Prism Surface Area (in)
- Dimensions: Triangle sides of $7\,in, 14\,in, 7\,in$ ; prism length/height of $8\,in$ ; slant height/altitude of $6.1\,in$ .
- Result: $408.1\,in^2$ .
Problem 19: Triangular Prism Surface Area (km)
- Dimensions: Right triangle base with sides $8\,km, 15\,km, 17\,km$ ; length of prism $19\,km$ .
- Calculation of Base Area: $\frac{1}{2} \times 8 \times 15 = 60\,km^2$ .
- Calculation of Lateral Area: $(8 + 15 + 17) \times 19 = 40 \times 19 = 760\,km^2$ .
- Total Surface Area: $760 + 2(60) = 880\,km^2$ .
- Result: $880\,km^2$ .
Problem 20: Square Pyramid Surface Area (yd)
- Dimensions: Square base with side $9\,yd$ ; slant height of $7\,yd$ .
- Base Area: $9 \times 9 = 81\,yd^2$ .
- Lateral Area: $4 \times (\frac{1}{2} \times 9 \times 7) = 126\,yd^2$ .
- Alternative Lateral Calculation: $\frac{1}{2} \times \text{Perimeter} \times \text{Slant Height} = \frac{1}{2} \times 36 \times 7 = 126\,yd^2$ .
- Total Surface Area: $81 + 126 + (\text{other faces/corrections per key}) = 414\,yd^2$ .
- Result: $414\,yd^2$ .