Printable math worksheet for calculating surface area of prisms and cylinders.

Here are the step-by-step solutions for finding the exact surface area of each shape.

1) Rectangular Prism
* Dimensions: Length = 6 ft, Width = 5 ft, Height = 12 ft.
* Formula: $2(lw + lh + wh)$
* Calculation:
* Top/Bottom: $6 \times 5 = 30$
* Front/Back: $6 \times 12 = 72$
* Sides: $5 \times 12 = 60$
* Sum: $30 + 72 + 60 = 162$
* Total Surface Area: $162 \times 2 = 324$
* Answer: 324 sq ft

2) Triangular Prism
* Dimensions: Triangle base = 6 yd, Triangle height = 4 yd, Triangle sides = 5 yd, Prism length = 11 yd.
* Parts: 2 triangular bases and 3 rectangular faces.
* Calculation:
* Two Triangles: Area = $\frac{1}{2} \times \text{base} \times \text{height}$. So, $2 \times (\frac{1}{2} \times 6 \times 4) = 24$ sq yd.
* Bottom Rectangle: $6 \times 11 = 66$ sq yd.
* Side Rectangles: $5 \times 11 = 55$ sq yd. There are two of these, so $55 \times 2 = 110$ sq yd.
* Total: $24 + 66 + 110 = 200$
* Answer: 200 sq yd

3) Rectangular Prism
* Dimensions: Length = 8 in, Width = 14 in, Height = 12 in.
* Formula: $2(lw + lh + wh)$
* Calculation:
* Top/Bottom: $8 \times 14 = 112$
* Front/Back: $8 \times 12 = 96$
* Sides: $14 \times 12 = 168$
* Sum: $112 + 96 + 168 = 376$
* Total Surface Area: $376 \times 2 = 752$
* Answer: 752 sq in

4) Triangular Prism
* Dimensions: Triangle legs = 9 in and 12 in, Hypotenuse = 15 in, Prism length = 9 in.
* Parts: 2 triangular bases and 3 rectangular faces.
* Calculation:
* Two Triangles: Area = $\frac{1}{2} \times 9 \times 12 = 54$. Two of them is $54 \times 2 = 108$ sq in.
* Bottom Rectangle: $12 \times 9 = 108$ sq in.
* Back Rectangle: $9 \times 9 = 81$ sq in.
* Slanted Rectangle: $15 \times 9 = 135$ sq in.
* Total: $108 + 108 + 81 + 135 = 432$
* Answer: 432 sq in

5) Cube
* Dimensions: Side = 9 m.
* Formula: $6 \times s^2$ (since all 6 faces are squares).
* Calculation:
* Area of one face: $9 \times 9 = 81$ sq m.
* Total Surface Area: $81 \times 6 = 486$
* Answer: 486 sq m

6) Cylinder
* Dimensions: Radius ($r$) = 10 yd, Height ($h$) = 16 yd.
* Formula: $2\pi r^2 + 2\pi rh$ (Two circles + side rectangle).
* Calculation:
* Two Circles (Bases): $2 \times \pi \times 10^2 = 2 \times \pi \times 100 = 200\pi$.
* Side (Lateral Area): $2 \times \pi \times 10 \times 16 = 320\pi$.
* Total: $200\pi + 320\pi = 520\pi$.
* Answer: $520\pi$ sq yd (or approx. 1,633.6 sq yd)

7) Cylinder
* Dimensions: Diameter = 2 in (so Radius $r = 1$ in), Height ($h$) = 11 in.
* Formula: $2\pi r^2 + 2\pi rh$.
* Calculation:
* Two Circles (Bases): $2 \times \pi \times 1^2 = 2\pi$.
* Side (Lateral Area): $2 \times \pi \times 1 \times 11 = 22\pi$.
* Total: $2\pi + 22\pi = 24\pi$.
* Answer: $24\pi$ sq in (or approx. 75.4 sq in)

8) Rectangular Prism
* Dimensions: Length = 7 ft, Width = 7 ft, Height = 14 ft.
* Formula: $2(lw + lh + wh)$
* Calculation:
* Top/Bottom: $7 \times 7 = 49$
* Front/Back: $7 \times 14 = 98$
* Sides: $7 \times 14 = 98$
* Sum: $49 + 98 + 98 = 245$
* Total Surface Area: $245 \times 2 = 490$
* Answer: 490 sq ft

9) Triangular Prism
* Dimensions: Triangle base = 10 yd, Triangle height = 12 yd, Triangle sides = 13 yd, Prism length = 14 yd.
* Parts: 2 triangular bases and 3 rectangular faces.
* Calculation:
* Two Triangles: Area = $\frac{1}{2} \times 10 \times 12 = 60$. Two of them is $60 \times 2 = 120$ sq yd.
* Bottom Rectangle: $10 \times 14 = 140$ sq yd.
* Side Rectangles: $13 \times 14 = 182$ sq yd. There are two of these, so $182 \times 2 = 364$ sq yd.
* Total: $120 + 140 + 364 = 624$
* Answer: 624 sq yd

Final Answer:
1) 324 sq ft
2) 200 sq yd
3) 752 sq in
4) 432 sq in
5) 486 sq m
6) $520\pi$ sq yd
7) $24\pi$ sq in
8) 490 sq ft
9) 624 sq yd