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

Here are the step-by-step solutions to find the exact surface area for each shape.

1) Rectangular Prism
* Formula: $2(lw + lh + wh)$
* Dimensions: Length = 6 ft, Width = 7 ft, Height = 12 ft
* Calculation:
* Front/Back: $6 \times 12 = 72$
* Top/Bottom: $6 \times 7 = 42$
* Sides: $7 \times 12 = 84$
* Sum: $72 + 42 + 84 = 198$
* Total Surface Area: $198 \times 2 = 396$
* Answer: 396 sq ft

2) Triangular Prism
* Faces: 2 Triangles (bases) and 3 Rectangles (sides).
* Triangle Dimensions: Base = 6 yd, Height = 4 yd. Side lengths = 5 yd.
* Prism Length: 11 yd.
* Calculation:
* Area of 2 Triangles: $2 \times (\frac{1}{2} \times 6 \times 4) = 24$ sq yd.
* Bottom Rectangle: $6 \times 11 = 66$ sq yd.
* Two Slanted Rectangles: $2 \times (5 \times 11) = 110$ sq yd.
* Total: $24 + 66 + 110 = 200$
* Answer: 200 sq yd

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

4) Triangular Prism
* Faces: 2 Triangles and 3 Rectangles.
* Triangle Dimensions: Base = 12 in, Height = 9 in. Hypotenuse = 15 in.
* Prism Length: 9 in.
* Calculation:
* Area of 2 Triangles: $2 \times (\frac{1}{2} \times 12 \times 9) = 108$ sq in.
* Bottom Rectangle: $12 \times 9 = 108$ sq in.
* Back Vertical 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
* Formula: $6 \times s^2$ (since all sides are equal squares)
* Side Length: 9 m
* Calculation:
* Area of one face: $9 \times 9 = 81$
* Total Surface Area: $81 \times 6 = 486$
* Answer: 486 sq m

6) Cylinder
* Formula: $2\pi r^2 + 2\pi rh$ (Area of two circles + Area of the side rectangle)
* Dimensions: Radius ($r$) = 10 yd, Height ($h$) = 10 yd.
* Calculation:
* Two Circles: $2 \times \pi \times 10^2 = 200\pi$
* Side Rectangle (Circumference $\times$ Height): $(2 \times \pi \times 10) \times 10 = 200\pi$
* Total: $200\pi + 200\pi = 400\pi$
* Answer: $400\pi$ sq yd (or approx. 1,256.64 sq yd)

7) Cylinder
* Formula: $2\pi r^2 + 2\pi rh$
* Dimensions: Diameter = 7 in, so Radius ($r$) = 3.5 in. Height ($h$) = 11 in.
* Calculation:
* Two Circles: $2 \times \pi \times 3.5^2 = 2 \times \pi \times 12.25 = 24.5\pi$
* Side Rectangle: $2 \times \pi \times 3.5 \times 11 = 77\pi$
* Total: $24.5\pi + 77\pi = 101.5\pi$
* Answer: $101.5\pi$ sq in (or approx. 318.87 sq in)

8) Square Prism (Rectangular Prism)
* Formula: $2(lw + lh + wh)$
* Dimensions: Length = 14 ft, Width = 7 ft, Height = 7 ft
* Calculation:
* Front/Back (Squares): $7 \times 7 = 49$. Two of them: $98$.
* Top/Bottom: $14 \times 7 = 98$. Two of them: $196$.
* Sides: $14 \times 7 = 98$. Two of them: $196$.
* Total: $98 + 196 + 196 = 490$
* Answer: 490 sq ft

9) Triangular Prism
* Faces: 2 Triangles and 3 Rectangles.
* Triangle Dimensions: Base = 10 yd, Height = 12 yd. Side lengths = 13 yd.
* Prism Length: 14 yd.
* Calculation:
* Area of 2 Triangles: $2 \times (\frac{1}{2} \times 10 \times 12) = 120$ sq yd.
* Bottom Rectangle: $10 \times 14 = 140$ sq yd.
* Two Slanted Rectangles: $2 \times (13 \times 14) = 2 \times 182 = 364$ sq yd.
* Total: $120 + 140 + 364 = 624$
* Answer: 624 sq yd

Final Answer:
1) 396 sq ft
2) 200 sq yd
3) 752 sq in
4) 432 sq in
5) 486 sq m
6) $400\pi$ sq yd
7) $101.5\pi$ sq in
8) 490 sq ft
9) 624 sq yd