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First, look closely: After zooming in on the eighth shape, I can identify it as a trapezoidal prism. The diagram shows that its trapezoidal bases have parallel sides of 10 cm and 6 cm, with a height (the perpendicular distance between them) of 4 cm. The length (or height) of the prism is 8 cm. To find the surface area, I need to calculate the area of the two trapezoidal bases and the four rectangular lateral faces. The formula for the surface area is $A = 2 \times \text{Base Area} + \text{Lateral Surface Area}$. I will now calculate the base area using the trapezoid area formula and then calculate the lateral area.
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Next, find information: I will now perform the calculation for the surface area of the trapezoidal prism.
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Then, review the findings: I have calculated the surface area for all eight shapes. I will now compile the final list of answers.
1. Cone (d=6 ft, l=10 ft): 122.46 ft²
2. Triangular Prism (sides 6, 8, 10 ft; length 12 ft): 288 ft²
3. Sphere (d=14 in): 615.44 in²
4. Cylinder (d=8 ft, h=12 ft): 401.92 ft²
5. Rectangular Prism (10x6x4 ft): 248 ft²
6. Cone (r=5 in, l=13 in): 282.6 in²
7. Rectangular Prism (15x8x6 cm): 516 cm²
8. Trapezoidal Prism (bases 10x6 cm, height 4 cm, length 8 cm): 320 cm²
Parent Tip: Review the logic above to help your child master the concept of surface area and volume practice worksheet.
