Surface Area of Prisms and Cylinders Worksheets - Free Printable

Here are the step-by-step solutions for each shape on the worksheet. We will use $\pi = 3.14$ for any calculations involving circles.

1) Triangular Prism
* Base Area: The base is a triangle with base 12 and height 5.
Area $= \frac{1}{2} \times 12 \times 5 = 30$. Since there are two bases (top and bottom), total base area $= 30 \times 2 = 60$.
* Lateral Area: The perimeter of the triangular base is $5 + 12 + 13 = 30$. The length of the prism is 8.
Lateral Area $= 30 \times 8 = 240$.
* Total Surface Area: $60 + 240 = 300$.

2) Rectangular Prism
* Dimensions: Length ($l$) = 10, Width ($w$) = 4, Height ($h$) = 3.
* Formula: $SA = 2(lw + lh + wh)$
* Calculation:
$lw = 10 \times 4 = 40$
$lh = 10 \times 3 = 30$
$wh = 4 \times 3 = 12$
Sum $= 40 + 30 + 12 = 82$
Total SA $= 2 \times 82 = 164$.

3) Rectangular Prism
* Dimensions: Length ($l$) = 9, Width ($w$) = 5, Height ($h$) = 4.
* Formula: $SA = 2(lw + lh + wh)$
* Calculation:
$lw = 9 \times 5 = 45$
$lh = 9 \times 4 = 36$
$wh = 5 \times 4 = 20$
Sum $= 45 + 36 + 20 = 101$
Total SA $= 2 \times 101 = 202$.

4) Cylinder
* Radius ($r$) = 3, Height ($h$) = 7.
* Formula: $SA = 2\pi r^2 + 2\pi rh$
* Base Area: $2 \times 3.14 \times 3^2 = 2 \times 3.14 \times 9 = 56.52$.
* Lateral Area: $2 \times 3.14 \times 3 \times 7 = 6.28 \times 21 = 131.88$.
* Total SA: $56.52 + 131.88 = 188.4$.

5) Rectangular Prism
* Dimensions: Length ($l$) = 6, Width ($w$) = 6, Height ($h$) = 10.
* Formula: $SA = 2(lw + lh + wh)$
* Calculation:
$lw = 6 \times 6 = 36$
$lh = 6 \times 10 = 60$
$wh = 6 \times 10 = 60$
Sum $= 36 + 60 + 60 = 156$
Total SA $= 2 \times 156 = 312$.

6) Trapezoidal Prism
* Base Area: The base is a trapezoid with parallel sides 4 and 10, and height 4.
Area of one base $= \frac{4 + 10}{2} \times 4 = 7 \times 4 = 28$.
Two bases $= 28 \times 2 = 56$.
* Lateral Area: Perimeter of the trapezoid base $= 4 + 5 + 10 + 5 = 24$. The length of the prism is 12.
Lateral Area $= 24 \times 12 = 288$.
* Total Surface Area: $56 + 288 = 344$.

7) Triangular Prism
* Base Area: The base is a triangle with base 10 and height 12.
Area of one base $= \frac{1}{2} \times 10 \times 12 = 60$.
Two bases $= 60 \times 2 = 120$.
* Lateral Area: The side lengths of the triangle are 13, 13, and 10. Perimeter $= 13 + 13 + 10 = 36$. The length of the prism is 15.
Lateral Area $= 36 \times 15 = 540$.
* Total Surface Area: $120 + 540 = 660$.

8) Rectangular Prism
* Dimensions: Length ($l$) = 12, Width ($w$) = 5, Height ($h$) = 8.
* Formula: $SA = 2(lw + lh + wh)$
* Calculation:
$lw = 12 \times 5 = 60$
$lh = 12 \times 8 = 96$
$wh = 5 \times 8 = 40$
Sum $= 60 + 96 + 40 = 196$
Total SA $= 2 \times 196 = 392$.

9) Trapezoidal Prism
* Base Area: The base is a trapezoid with parallel sides 3 and 7, and height 4.
Area of one base $= \frac{3 + 7}{2} \times 4 = 5 \times 4 = 20$.
Two bases $= 20 \times 2 = 40$.
* Lateral Area: Perimeter of the trapezoid base $= 3 + 5 + 7 + 5 = 20$. The length of the prism is 9.
Lateral Area $= 20 \times 9 = 180$.
* Total Surface Area: $40 + 180 = 220$.

Final Answer:
1) 300
2) 164
3) 202
4) 188.4
5) 312
6) 344
7) 660
8) 392
9) 220