Practice: Area, Surface Area & Volume

Grade 6 Mathematics | Independent Practice

Name:
Date:
Formula Reference: Triangle: A = (1/2)bh | Parallelogram: A = bh | Trapezoid: A = (1/2)(b1+b2)h | Volume: V = lwh | Surface Area: SA = 2lw + 2lh + 2wh

Part A: Area of Triangles

Directions: Find the area of each triangle. Remember: A = (1/2) x base x height

1. Base = 10 cm, Height = 6 cm

Area = cm^2

2. Base = 14 in, Height = 9 in

Area = in^2

3. Base = 8.5 m, Height = 4 m

Area = m^2

4. Base = 15 ft, Height = 12 ft

Area = ft^2

Part B: Area of Parallelograms and Trapezoids

Directions: Find the area. Use the correct formula for each shape.

5. Parallelogram: Base = 12 cm, Height = 7 cm

Area = cm^2

6. Trapezoid: Base 1 = 8 in, Base 2 = 14 in, Height = 6 in

Area = in^2

7. Parallelogram: Base = 9.5 m, Height = 8 m

Area = m^2

8. Trapezoid: Base 1 = 5 ft, Base 2 = 11 ft, Height = 4 ft

Area = ft^2

Part C: Surface Area of Rectangular Prisms

Directions: Find the surface area. SA = 2lw + 2lh + 2wh. Show your work.

9. Length = 6 cm, Width = 4 cm, Height = 3 cm

Surface Area = 2(___x___) + 2(___x___) + 2(___x___) = cm^2

10. Length = 10 in, Width = 5 in, Height = 8 in

Surface Area = in^2

11. A cube has sides of 7 cm each. (Hint: all sides are equal!)

Surface Area = cm^2

Part D: Volume of Rectangular Prisms

Directions: Find the volume. V = length x width x height

12. L = 5 cm, W = 4 cm, H = 6 cm

Volume = cm^3

13. L = 12 in, W = 3 in, H = 4 in

Volume = in^3

14. L = 8 m, W = 8 m, H = 2 m

Volume = m^3

15. A cube with side = 5 ft

Volume = ft^3

Part E: Real-World Problems

Directions: Read each problem. Show your work and include correct units.

16. A triangular sail has a base of 4 meters and a height of 6 meters. How much fabric is needed to make the sail?

Answer:

17. A shipping box measures 15 inches long, 10 inches wide, and 8 inches tall. How much cardboard is needed to make the box? (Find surface area)

Answer:

18. A fish tank is 24 inches long, 12 inches wide, and 16 inches tall. How many cubic inches of water can the tank hold? (Find volume)

Answer:

19. A garden bed shaped like a trapezoid has parallel sides of 6 feet and 10 feet, with a height of 4 feet. What is the area of the garden bed?

Answer:

Challenge: Think About It!

20. A rectangular prism has a volume of 120 cubic cm. The length is 6 cm and the width is 4 cm. What is the height?

Height = cm

Hint: If V = l x w x h, then h = V / (l x w)

21. Which has greater volume: a box that is 10 x 5 x 4 inches, or a box that is 8 x 8 x 3 inches?

Box 1 volume: _______ in^3    Box 2 volume: _______ in^3

The _____________ box has greater volume.